Koszul Duality Patterns in Representation Theory

From MaRDI portal
Publication:4874244

DOI10.1090/S0894-0347-96-00192-0zbMath0864.17006OpenAlexW1519011338MaRDI QIDQ4874244

Wolfgang Soergel, Victor Ginzburg, Alexander A. Beilinson

Publication date: 22 June 1997

Published in: Journal of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0894-0347-96-00192-0



Related Items

Exact Hochschild extensions and deformed Calabi-Yau completions, Kazhdan-Lusztig polynomials and character formulae for the Lie superalgebra đ”€đ”©(đ”Ș|đ”«), A Topological Approach to Soergel Theory, A Koszul duality for props, Co-Point Modules Over Frobenius Koszul Algebras, Cell complexes, poset topology and the representation theory of algebras arising in algebraic combinatorics and discrete geometry, Quantum groups, the loop Grassmannian, and the Springer resolution, The cohomology of certain Hopf algebras associated with 𝑝-groups, The many integral graded cellular bases of Hecke algebras of complex reflection groups, Category đ’Ș: Quivers and endomorphism rings of projectives, Unnamed Item, Symplectic resolutions, symplectic duality, and Coulomb branches, K$K$‐Motives and Koszul duality, Yoneda algebras and their singularity categories, Cohomology in singular blocks of parabolic category, A geometric Steinberg formula, Tensor product algebras, Grassmannians and Khovanov homology, Differential graded Koszul duality: An introductory survey, Modular Koszul duality for Soergel bimodules, Shift modules, strongly stable ideals, and their dualities, Interactions between algebraic geometry and noncommutative algebra. Abstracts from the workshop held May 1--7, 2022, Perverse monodromic sheaves, Duality between Lagrangian and Legendrian invariants, ON GRADED SYMMETRIC CELLULAR ALGEBRAS, On minimal tilting complexes in highest weight categories, Kazhdan-Lusztig algorithm for Whittaker modules with arbitrary infinitesimal characters, Whittaker categories, properly stratified categories and Fock space categorification for Lie superalgebras, A category \(\mathcal{O}\) for oriented matroids, The affine Grassmannian and the Springer resolution in positive characteristic, Working session: Geometric representation theory. Abstracts from the working session held April 3--9, 2022, On one-sided singular Soergel bimodules, Reductions of triangulated categories and simple‐minded collections, Preprojective algebras of \(d\)-representation finite species with relations, Bott-Samelson-Demazure-Hansen varieties for projective homogeneous varieties with nonreduced stabilizers, Koszul monoids in quasi-abelian categories, K‐theory Soergel bimodules, Parabolic category for periplectic Lie superalgebras, â„€ Q type constructions in higher representation theory, Categorification: tangle invariants and TQFTs, Classification results for \(n\)-hereditary monomial algebras, Equivariant resolutions over Veronese rings, PERVERSE MOTIVES AND GRADED DERIVED CATEGORY, THE LOEWY STRUCTURE OF -VERMA MODULES OF SINGULAR HIGHEST WEIGHTS, Notes on the Geometric Satake Equivalence, Homological properties of sklyanin algebras, NODE DELETION AND STABLY EQUIVALENT KOSZUL ALGEBRAS, A new approach to the Koszul property in representation theory using graded subalgebras, A generalized Koszul theory and its application, The derived category of an algebra with radical square zero, McCoy rings of path algebras and truncated algebras, Knot invariants and higher representation theory, Some Homological Properties of Tensor and Wreath Products of Quasi-Hereditary Algebras, ON THE EXISTENCE OF A DERIVED EQUIVALENCE BETWEEN A KOSZUL ALGEBRA AND ITS YONEDA ALGEBRA, MODULES WITH PURE RESOLUTIONS OVER KOSZUL ALGEBRAS, GRADED CARTAN MATRICES OF DEFECT 2 BLOCKS OF SYMMETRIC GROUPS, Translation and shuffling of projectively presentable modules and a categorification of a parabolic Hecke module, Existence of Gradings on Associative Algebras, On a Group Graded Version of BGG, On the quasi-hereditary property for staggered sheaves, Canonical bases and higher representation theory, Koszulity for nonquadratic algebras., THE ODD PART OF ANn-KOSZUL ALGEBRA, A categorification of integral Specht modules, Categorical Langlands correspondence for 𝑆𝑂_{𝑛,1}(ℝ), Cherednik algebras and Hilbert schemes in characteristic 𝑝, A category for the adjoint representation, Graded Specht modules, Modular perverse sheaves on flag varieties. II: Koszul duality and formality., Batalin-Vilkovisky algebras and the noncommutative PoincarĂ© duality of Koszul Calabi-Yau algebras, Intersection cohomology of the symmetric reciprocal plane, Bar operators for quasiparabolic conjugacy classes in a Coxeter group., On \(n\)-translation algebras, Mixed Perverse Sheaves on Flag Varieties for Coxeter Groups, Koszul duality for Iwasawa algebras modulo 𝑝, Generating the Fukaya categories of Hamiltonian đș-manifolds, Koszul duality for Kac–Moody groups and characters of tilting modules, Higher preprojective algebras, Koszul algebras, and superpotentials, ÎŽ-Koszul Algebras, Algebraic properties of zigzag algebras, The Orlik-Terao Algebra and the Cohomology of Configuration Space, Koszulity of some path categories, Koszulity for graded skew PBW extensions, Koszulness and supersolvability for Dirichlet arrangements, Lifts of longest elements to braid groups acting on derived categories, Some geometric facets of the Langlands correspondence for real groups, Quiver Schur algebras for linear quivers, WHEN ARE THERE ENOUGH PROJECTIVE PERVERSE SHEAVES?, (Contravariant) Koszul Duality for DG Algebras, Kronecker positivity and 2-modular representation theory, Representations of modular skew group algebras, On Koszulity of finite graded posets, Koszulity and Koszul modules of dual extension algebras, Preresolutions of noncommutative isolated singularities, Intersection cohomology of moduli spaces of sheaves on surfaces, \(d\)-Koszul algebras., Koszul duality for semidirect products and generalized Takiff algebras, Homotopy Lie algebras; lower central series and the Koszul property, Finite generation of Ext for a generalization of \(D\)-Koszul algebras., Equivariant-constructible Koszul duality for dual toric varieties, Derived representation theory of Lie algebras and stable homotopy categorification of \(sl_{k}\), Rationality of the PoincarĂ© series for Koszul algebras., A Lie theoretic categorification of the coloured Jones polynomial, Essential orders on stratified algebras with duality and \(\mathcal{S}\)-subcategories in \(\mathcal{O}\), A structure theorem for Harish-Chandra bimodules via coinvariants and Golod rings, Deformations of Koszul Artin-Schelter Gorenstein algebras., Boundaries, mirror symmetry, and symplectic duality in \(3d \mathcal{N}=4 \) gauge theory, Categorified skew Howe duality and comparison of knot homologies, \(t\)-structures on some local Calabi--Yau varieties, Nazarov-Wenzl algebras, coideal subalgebras and categorified skew Howe duality, Frobenius semisimplicity for convolution morphisms, Translation quiver varieties, Koszulity of cohomology \( = K(\pi,1)\)-Ness + quasi-formality, PBW-deformations of graded rings, Batalin-Vilkovisky structure on Hochschild cohomology of zigzag algebra of type \(\widetilde{\mathbf{A}}_1\), Contravariant pairings between standard Whittaker modules and Verma modules, A geometric construction of colored HOMFLYPT homology, Mixed tensors of the general linear supergroup, Koszul duality patterns in Floer theory, Local Hodge theory of Soergel bimodules, Rock blocks, wreath products and KLR algebras, Dirac cohomology of highest weight modules, The classification of blocks in BGG category \(\mathcal{O}\), Generalizations of Lie algebras, Basic structures on derived critical loci, Projective modules in the category \(\mathcal O\) for the Cherednik algebra., Some examples of \(t\)-structures for finite-dimensional algebras, Quasi-hereditary covers of higher zigzag algebras of type \(A\), On graded Frobenius algebras, Category \({\mathcal O}\): gradings and translation functors., Koszulity of directed categories in representation stability theory, PoincarĂ©-Birkhoff-Witt deformation of Koszul Calabi-Yau algebras., Tilting modules in category \(\mathcal O\) and sheaves on moment graphs, Ringel duality for perverse sheaves on hypertoric varieties, The Khovanov-Lauda 2-category and categorifications of a level two quantum \(\mathfrak{sl}_n\) representation, \((p,\lambda)\)-Koszul algebras and modules., Gale duality and Koszul duality, Characters for projective modules in the BGG category \(\mathcal{O}\) for the orthosymplectic Lie superalgebra \(\mathfrak{osp}(3 | 4)\), BGG complexes in singular blocks of category \(\mathcal{O}\), Koszul algebras and quadratic duals in Galois cohomology, Generic and \(q\)-rational representation theory, Universal tensor categories generated by dual pairs, Whittaker coinvariants for \(\mathrm{GL}(m|n)\), Some homological properties of category \(\mathcal{O}\). VI, From simple-minded collections to silting objects via Koszul duality, Ordered tensor categories and representations of the Mackey Lie algebra of infinite matrices, Mixed motives and geometric representation theory in equal characteristic, Koszul algebras and flow lattices, Koszul duality for quasi-split real groups, \(n\)-APR tilting and \(\tau\)-mutations, Equivariant perverse sheaves and quasi-hereditary algebras, Hochschild cohomology of polynomial representations of \(\mathrm{GL}_2\), The algebraic geometry of Kazhdan-Lusztig-Stanley polynomials, Koszul duality of affine Kac-Moody algebras and cyclotomic rational double affine Hecke algebras, New criteria for \(\lambda\)-Koszul algebras., Nonpure piecewise-Koszul algebras., Categorification of tensor product representations of \(\mathfrak{sl}_k\) and category \(\mathcal{O}\), Category \(\mathcal O\) over a deformation of the symplectic oscillator algebra., Categorification of the Temperley-Lieb category, tangles, and cobordisms via projective functors, Representation type of the blocks of category \(\mathcal O_S\) in types \(F_{4}\) and \(G_{2}\), On category \(\mathcal O\) for cyclotomic rational Cherednik algebras., Some Koszul rings from geometry, Finitistic dimension and tilting modules for stratified algebras., Tensor representations of \(\mathfrak{q} (\infty )\), On trivial extensions and higher preprojective algebras, Symmetric structure for the endomorphism algebra of projective-injective module in parabolic category, Reductive groups, the loop Grassmannian, and the Springer resolution, Bigrassmannian permutations and Verma modules, On \(n\)-slice algebras and related algebras, Preprojective algebra structure on skew-group algebras, Two-block Springer fibers of types C and D: a diagrammatic approach to Springer theory, On computer-assisted research in homological algebra., Projective modules over classical Lie algebras of infinite rank in the parabolic category, Koszul duality for compactly generated derived categories of second kind, Motivic Springer theory, A vanishing result for higher smooth duals, Jantzen coefficients and simplicity of parabolic Verma modules, An Iwahori-Whittaker model for the Satake category, Canonical resolutions over Koszul algebras, Pertinency of Hopf actions and quotient categories of Cohen-Macaulay algebras, Categorical Koszul duality, Coherent categorification of quantum loop algebras: the \(\operatorname{SL}(2)\) case, Constructible sheaves on affine Grassmannians and geometry of the dual nilpotent cone, The Brundan-Kazhdan-Lusztig conjecture for general linear Lie superalgebras, Translation algebras and their applications., Smith-Treumann theory and the linkage principle, Koszul dual 2-functors and extension algebras of simple modules for \(\mathrm{GL}_2\)., Character formulas in category \(\mathcal{O}\) for exceptional Lie superalgebra \(G(3)\), Homotopy-theoretically enriched categories of noncommutative motives, Integral motivic sheaves and geometric representation theory, Homogeneous algebras., Noncommutative (crepant) desingularizations and the global spectrum of commutative rings, On the Relation Between Finitistic and Good Filtration Dimensions, Unnamed Item, Embedding a quantum rank three quadric in a quantum P3, Unnamed Item, Highest weight categories arising from Khovanov’s diagram algebra III: category đ’Ș, Graded decomposition matrices of 𝑣-Schur algebras via Jantzen filtration, Dualities and derived equivalences for category \(\mathcal{O}\), Lower central series and free resolutions of hyperplane arrangements, Homological Mirror Symmetry for the genus two curve, Rings Defined by Extensions, Connected cochain DG algebras of Calabi-Yau dimension 0, Hochschild (co)homology of Yoneda algebras of reconstruction algebras of type A 1, Fayers’ conjecture and the socles of cyclotomic Weyl modules, Koszul duality for stratified algebras. I: Balanced quasi-hereditary algebras., A PoincarĂ©-Birkhoff-Witt theorem for quadratic algebras with group actions, Loewy series of parabolically induced -Verma modules, Shuffling functors and spherical twists on \(D^{\mathrm{b}}(\mathcal{O}_0)\), Some homological properties of category \(\mathcal{O}\). IV, Diagram categories for \(\mathrm{U}_q\)-tilting modules at roots of unity, Comparison of canonical bases for Schur and universal enveloping algebras, Homological mirror symmetry of elementary birational cobordisms, Unnamed Item, Kazhdan-Lusztig conjecture via zastava spaces, Monodromic model for Khovanov-Rozansky homology, Exploring Noncommutative Algebras via Deformation Theory, Higher zigzag algebras, Mild pro-\(p\) groups and the Koszulity conjectures, Modular perverse sheaves on flag varieties III: Positivity conditions, Classifying torsion classes for algebras with radical square zero via sign decomposition, Positroids, knots, and \(q,t\)-Catalan numbers, ROUQUIER’S CONJECTURE AND DIAGRAMMATIC ALGEBRA, Generalized Koszul algebra and Koszul duality, Koszul duality and Soergel bimodules for dihedral groups, Cohomology of tilting modules over quantum groups and \(t\)-structures on derived categories of coherent sheaves, Koszul duality in quantum field theory, Algebraic deformations of toric varieties. I: General constructions, The Weyl extension algebra of \(GL_2(\overline{\mathbb F}_p)\)., McKay quivers and Lusztig algebras of some finite groups, Differential projective modules over algebras with radical square zero, Projective-injective modules, Serre functors and symmetric algebras, Unnamed Item, Wall-Crossing functors and D-modules, Quasi-hereditary algebras and generalized Koszul duality., Super duality and Kazhdan-Lusztig polynomials, HOCHSCHILD (CO)HOMOLOGY OF â„€2Ă—â„€2-GALOIS COVERINGS OF QUANTUM EXTERIOR ALGEBRAS, Cocycle twists of algebras, On monoidal Koszul duality for the Hecke category, A duality theorem for generalized Koszul algebras., Weighted locally gentle quivers and Cartan matrices., A criterion for Gorenstein algebras to be regular, Hochschild cohomology of group extensions of quantum symmetric algebras, Cohomology of 3-dimensional color Lie algebras, Linear Koszul duality, Some homological properties of the category đ’Ș, II, Twisted graded Hecke algebras., An algorithmic approach to resolutions, Weak projections onto a braided Hopf algebra., The Koszul dual of a weakly Koszul module., Cubist algebras., Kazhdan-Lusztig-Polynome und eine Kombinatorik fĂŒr Kipp-Moduln, Piecewise-Koszul algebras., \(N\)-homogeneous superalgebras., AUSLANDER ALGEBRAS ARE 2-GORENSTEIN, Mixed algebras and quivers related to cell complexes, Quivers, Floer cohomology, and braid group actions, Representation theory of symmetric groups and related Hecke algebras, Koszul configurations of points in projective spaces, Koszul Modules and Modules with Linear Presentations, Unnamed Item, Koszul and Gorenstein properties for homogeneous algebras., Castelnuovo-Mumford regularity for complexes and weakly Koszul modules., Supersolvability and the Koszul property of root ideal arrangements, On the category of Koszul modules of complexity one of an exterior algebra., A diagram algebra for Soergel modules corresponding to smooth Schubert varieties, PBW deformations of Koszul algebras over a nonsemisimple ring., Projective modules for the symmetric group and Young's seminormal form., Quadratic duals, Koszul dual functors, and applications, Kostant Modules in Blocks of Category đ’ȘS, Some homological properties of category \(\mathcal{O}\). III, COMBINATORICS AND N-KOSZUL ALGEBRAS, Sheaves on affine Schubert varieties, modular representations, and Lusztig’s conjecture, Sheaves of t-structures and valuative criteria for stable complexes, Koszul duality and equivalences of categories, On exotic and perverse-coherent sheaves, Koszul calculus of preprojective algebras, Two kinds of derived categories, Koszul duality, and comodule-contramodule correspondence, Parabolic category O, perverse sheaves on Grassmannians, Springer fibres and Khovanov homology, EQUATIONS FOR $\overline M_{0,n}$, On Koszul duality for Kac-Moody groups, Rock blocks, Representation type of the blocks of category \(\mathcal O_s\), Koszul duality for toric varieties, Full Graphs and Koszul Algebras I, Koszul modules, Intersection cohomology of hypertoric varieties, Homologie de hochschild des deformations quadratiques d’algebres de polynomes, Higher Koszul algebras and \(A\)-infinity algebras., Hochschild (Co)homology of Exterior Algebras, Homological degrees of representations of categories with shift functors, Modular Koszul duality, On weight modules of algebras of twisted differential operators on the projective space, Categorification of tensor powers of the vector representation of \(U_q(\mathfrak{gl}(1| 1))\), On quantized decomposition maps for graded algebras, Affine category \(\mathcal{O}\), Koszul duality and Zuckerman functors, The quantum Hikita conjecture, Bounded t-structures on the bounded derived category of coherent sheaves over a weighted projective line, Stable categories of graded maximal Cohen-Macaulay modules over noncommutative quotient singularities, DG Poisson algebra and its universal enveloping algebra, Perverse sheaves on affine flags and Langlands dual group, Koszul duality for operads, Parabolic projective functors in type \(A\), Notes on nonpure piecewise-Koszul algebras., Applications of the category of linear complexes of tilting modules associated with the category \(\mathcal O\), Algebras with periodic shifts of Ext degrees., Further properties and applications of Koszul pairs, Quivers with relations arising from Koszul algebras of \(\mathfrak g\)-invariants, Higher symplectic reflection algebras and non-homogeneous \(N\)-Koszul property., Affine Jacquet functors and Harish-Chandra categories, Koszul property of a class of graded algebras with nonpure resolutions, Eisenstein series and quantum groups, Singular blocks of restricted \(\mathfrak{sl}_3\), Connected braided Hopf algebras., Perverse sheaves, Koszul IC-modules, and the quiver for the category \(\mathcal{O}\), Koszul-like algebras and modules., Loop spaces and representations, Minimal free resolutions of determinantal ideals and irreducible representations of the Lie superalgebra \(gl(m\mid n)\), Closed form algebra on a disk is Koszul, Projective functors for algebraic groups., Primary ideals associated to the linear strands of Lascoux's resolution and syzygies of the corresponding irreducible representations of the Lie superalgebra \(\mathfrak {gl}(m|n)\), Representations of semisimple Lie algebras in prime characteristic and the noncommutative Springer resolution, The degenerate analogue of Ariki's categorification theorem, Noncommutative quadric surfaces, A numerical criterion for the generalized Koszul property., Koszul algebras and their ideals., Ringel duality and derivatives of non-additive functors, Graded and Koszul categories, Quiver Schur algebras and Koszul duality., Returning arrows for self-injective algebras and Artin-Schelter regular algebras., Singular localization of \(\mathfrak{g}\)-modules and applications to representation theory, Highest weight categories arising from Khovanov's diagram algebra. IV: The general linear supergroup, Categorifying fractional Euler characteristics, Jones-Wenzl projectors and \(3j\)-symbols, Equivariant sheaves on flag varieties, A Koszul category of representations of finitary Lie algebras, Group actions on algebras and the graded Lie structure of Hochschild cohomology., On category \(\mathcal O\) over triangular generalized Weyl algebras., Gradings on walled Brauer algebras and Khovanov's arc algebra, Discrete Koszul algebras., Hypertoric category \(\mathcal O\)., Singular blocks of parabolic category \(\mathcal O\) and finite \(W\)-algebras, Koszul duality and semisimplicity of Frobenius, Categorification of the Catalan monoid., Heegaard Floer homology as morphism spaces, Perfect derived categories of positively graded DG algebras, Categories of modules over an affine Kac-Moody algebra and finiteness of the Kazhdan-Lusztig tensor product, Skew group algebras of Calabi-Yau algebras., Tilting equivalences: from hereditary algebras to symmetric groups., Auslander-Reiten sequences and \(t\)-structures on the homotopy category of an Abelian category., Grassmannians and Koszul duality, Weighted blowups and mirror symmetry for toric surfaces, Unicity of graded covers of the category \(\mathcal{O}\) of Bernstein-Gelfand-Gelfand, Orthosymplectic Lie superalgebras, Koszul duality, and a complete intersection analogue of the Eagon-Northcott complex, Type A blocks of super category \(\mathcal{O}\), Constructible sheaves on nilpotent cones in rather good characteristic, Categorification of (induced) cell modules and the rough structure of generalised Verma modules, Koszul-Morita duality, Sheaves on fibered threefolds and quiver sheaves, Koszul differential graded algebras and BGG correspondence., The bounded derived categories of an algebra with radical squared zero, Graded Brauer tree algebras., Noetherianity and Gelfand-Kirillov dimension of components., Cohomology of quantum groups at roots of unity, Highest weight categories arising from Khovanov's diagram algebra. II: Koszulity, On a common generalization of Koszul duality and tilting equivalence., Koszul duality in deformation quantization and Tamarkin's approach to Kontsevich formality, Cuspidal representations of \(\mathfrak{sl}(n+1)\), Hochschild cohomology rings of \(d\)-Koszul algebras., Loewy series of Weyl modules and the PoincarĂ© polynomials of quiver varieties, Faces of polytopes and Koszul algebras, Koszul incidence algebras, affine semigroups, and Stanley-Reisner ideals., Localization algebras and deformations of Koszul algebras., Coherent sheaves and categorical \(\mathfrak{sl}_2\) actions, Geometric Schur duality of classical type, Koszul duality for extension algebras of standard modules., A family of Koszul algebras arising from finite-dimensional representations of simple Lie algebras, Diagrammatic description for the categories of perverse sheaves on isotropic Grassmannians, Galois cohomology of a number field is Koszul, A generalized Koszul theory and its relation to the classical theory., Brundan-Kazhdan-Lusztig and super duality conjectures, Confluence and Koszulity, On modules with linear presentations, The minimal realization from deformation theory, \(A\)-infinity structures related to bi-Koszul algebras., Graded decomposition numbers for cyclotomic Hecke algebras., Parabolic generalization of Kazhdan-Lusztig polynomials and bases, Minimal resolutions of algebras, Graded, selfinjective, and Koszul algebras, Koszul differential graded modules., Hochschild (co)homology of Galois coverings of Grassmann algebras., Koszul algebras and finite Galois coverings., Quantized Koszul complexes



Cites Work