Highest weight categories arising from Khovanov's diagram algebra. II: Koszulity
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Publication:969613
DOI10.1007/s00031-010-9079-4zbMath1205.17010arXiv0806.3472OpenAlexW3104259847MaRDI QIDQ969613
Catharina Stroppel, Jonathan Brundan
Publication date: 7 May 2010
Published in: Transformation Groups (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/0806.3472
highest weight categoryKoszul algebraKazhdan-Lusztig polynomialprojective functorKhovanov's diagram algebraBGG resolutiondouble centralizer propertyKostant module
Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Quadratic and Koszul algebras (16S37)
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Highest weight categories arising from Khovanov’s diagram algebra III: category 𝒪 ⋮ Fukaya-Seidel categories of Hilbert schemes and parabolic category \(\mathcal{O}\) ⋮ MODULAR DECOMPOSITION NUMBERS OF CYCLOTOMIC HECKE AND DIAGRAMMATIC CHEREDNIK ALGEBRAS: A PATH THEORETIC APPROACH ⋮ Nazarov-Wenzl algebras, coideal subalgebras and categorified skew Howe duality ⋮ Khovanov-Seidel quiver algebras and Ozsváth-Szabó's bordered theory ⋮ Mixed tensors of the general linear supergroup ⋮ Deligne’s category \underline{𝑅𝑒}𝑝(𝐺𝐿_{𝛿}) and representations of general linear supergroups ⋮ Cellular structures using \(U_q\)-tilting modules ⋮ Diagram categories for \(\mathrm{U}_q\)-tilting modules at roots of unity ⋮ Idempotent subquotients of symmetric quasi-hereditary algebras. ⋮ A diagrammatic Temperley-Lieb categorification ⋮ The classification of blocks in BGG category \(\mathcal{O}\) ⋮ Bernstein-Gelfand-Gelfand resolutions for basic classical Lie superalgebras ⋮ Gruson-Serganova character formulas and the Duflo-Serganova cohomology functor ⋮ Cohomology in singular blocks of parabolic category ⋮ The \(\mathfrak{sl}_N\)-web algebras and dual canonical bases ⋮ Highest weight categories arising from Khovanov's diagram algebra. IV: The general linear supergroup ⋮ \(\mathrm{SL}_2\) tilting modules in the mixed case ⋮ Categorifying fractional Euler characteristics, Jones-Wenzl projectors and \(3j\)-symbols ⋮ On minimal tilting complexes in highest weight categories ⋮ Injective and tilting resolutions and a Kazhdan-Lusztig theory for the general linear and symplectic group ⋮ A combinatorial translation principle and diagram combinatorics for the symplectic group ⋮ Whittaker categories, properly stratified categories and Fock space categorification for Lie superalgebras ⋮ On the functoriality of \(\mathfrak{sl}_2\) tangle homology ⋮ A combinatorial translation principle and diagram combinatorics for the general linear group ⋮ UNITARY REPRESENTATIONS OF CYCLOTOMIC HECKE ALGEBRAS AT ROOTS OF UNITY: COMBINATORIAL CLASSIFICATION AND BGG RESOLUTIONS ⋮ Cuspidal \(\mathfrak{sl}_n\)-modules and deformations of certain Brauer tree algebras ⋮ On classical tensor categories attached to the irreducible representations of the general linear supergroups \(GL(n|n)\) ⋮ \(\mathfrak{sl}_N\)-web categories and categorified skew Howe duality ⋮ The Khovanov-Lauda 2-category and categorifications of a level two quantum \(\mathfrak{sl}_n\) representation ⋮ Gradings on walled Brauer algebras and Khovanov's arc algebra ⋮ The Blanchet-Khovanov algebras ⋮ Combinatorics of character formulas for the Lie superalgebra \(\mathfrak{gl}(m,n)\) ⋮ Standard Koszul standardly stratified algebras ⋮ Heisenberg and Kac-Moody categorification ⋮ Quantum link homology via trace functor. I ⋮ On the Ext algebras of parabolic Verma modules and \(A_{\infty}\)-structures ⋮ Diagrammatic Kazhdan-Lusztig theory for the (walled) Brauer algebra. ⋮ \(\mathfrak{sl}_3\)-web bases, intermediate crystal bases and categorification ⋮ Grassmannians and Koszul duality ⋮ Odd Khovanov's arc algebra ⋮ A new approach to the Koszul property in representation theory using graded subalgebras ⋮ Some homological properties of the category 𝒪, II ⋮ Whittaker modules for classical Lie superalgebras ⋮ The \(\mathfrak{sl}_3\)-web algebra ⋮ Thick ideals in Deligne's category \(\underline{\mathrm{Re}}\mathrm{p}(O_\delta)\) ⋮ The quantized walled Brauer algebra and mixed tensor space ⋮ Category \(\mathcal O\) for quantum groups ⋮ On supergroups and their semisimplified representation categories ⋮ Dominant dimension and almost relatively true versions of Schur's theorem. ⋮ A diagram algebra for Soergel modules corresponding to smooth Schubert varieties ⋮ Character and dimension formulae for queer Lie superalgebra ⋮ A Weyl-Type character formula for PDC modules of gl(m|n) ⋮ Pieri type rules and \(GL(2|2)\) tensor products ⋮ 𝔤𝔩n-webs, categorification and Khovanov–Rozansky homologies ⋮ On BGG resolutions of unitary modules for quiver Hecke and Cherednik algebras ⋮ Projective modules over classical Lie algebras of infinite rank in the parabolic category ⋮ Cohomological Tensor Functors on Representations of the General Linear Supergroup ⋮ Real Springer fibers and odd arc algebras ⋮ Quiver Schur algebras for linear quivers ⋮ The modular Weyl-Kac character formula ⋮ The representation theory of Brauer categories. I: triangular categories ⋮ An odd categorification of \(U_q(\mathfrak{sl}_2)\)
Cites Work
- Unnamed Item
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- Unnamed Item
- A functor-valued invariant of tangles
- A BGG-type resolution for tensor modules over general linear superalgebra
- Irreducible characters of semisimple Lie groups. II: The Kazhdan-Lusztig conjectures
- Representations of Coxeter groups and Hecke algebras
- A generalization of the Bernstein-Gelfand-Gelfand resolution
- Categorification of the Temperley-Lieb category, tangles, and cobordisms via projective functors
- Quasi-hereditary extension algebras.
- Koszul equivalences and dualities.
- On the Bernstein-Gelfand-Gelfand resolution for Kac-Moody algebras and quantized enveloping algebras
- Perverse Sheaves on Grassmannians
- Parabolic category O, perverse sheaves on Grassmannians, Springer fibres and Khovanov homology
- Quadratic duals, Koszul dual functors, and applications
- Kostant Modules in Blocks of Category 𝒪S
- The Homological Dual of a Highest Weight Category
- Kazhdan-Lusztig polynomials and character formulae for the Lie superalgebra 𝔤𝔩(𝔪|𝔫)
- Category 𝒪: Quivers and endomorphism rings of projectives
- Koszul Duality Patterns in Representation Theory
- Highest weight categories arising from Khovanov's diagram algebra I: cellularity
- Double centralizer properties, dominant dimension, and tilting modules
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