Category \({\mathcal O}\): gradings and translation functors.
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Publication:1409754
DOI10.1016/S0021-8693(03)00308-9zbMath1040.17002MaRDI QIDQ1409754
Publication date: 22 October 2003
Published in: Journal of Algebra (Search for Journal in Brave)
Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Graded rings and modules (associative rings and algebras) (16W50)
Related Items (37)
Categorification of tensor powers of the vector representation of \(U_q(\mathfrak{gl}(1| 1))\) ⋮ Affine category \(\mathcal{O}\), Koszul duality and Zuckerman functors ⋮ A Lie theoretic categorification of the coloured Jones polynomial ⋮ Dualities and derived equivalences for category \(\mathcal{O}\) ⋮ Parabolic projective functors in type \(A\) ⋮ Applications of the category of linear complexes of tilting modules associated with the category \(\mathcal O\) ⋮ On functors associated to a simple root ⋮ Nazarov-Wenzl algebras, coideal subalgebras and categorified skew Howe duality ⋮ Shuffling functors and spherical twists on \(D^{\mathrm{b}}(\mathcal{O}_0)\) ⋮ Cellular structures using \(U_q\)-tilting modules ⋮ Some homological properties of category \(\mathcal{O}\). IV ⋮ Diagram categories for \(\mathrm{U}_q\)-tilting modules at roots of unity ⋮ Koszul duality and Soergel bimodules for dihedral groups ⋮ Categorifying fractional Euler characteristics, Jones-Wenzl projectors and \(3j\)-symbols ⋮ On first extensions in \(\mathcal{S}\)-subcategories of \(\mathcal{O}\) ⋮ Categorification: tangle invariants and TQFTs ⋮ Homological invariants in category $\mathcal {O}$ for the general linear superalgebra ⋮ Tilting modules in category \(\mathcal O\) and sheaves on moment graphs ⋮ Projective-injective modules, Serre functors and symmetric algebras ⋮ Unnamed Item ⋮ The Khovanov-Lauda 2-category and categorifications of a level two quantum \(\mathfrak{sl}_n\) representation ⋮ Some homological properties of category \(\mathcal{O}\). VI ⋮ Some homological properties of the category 𝒪, II ⋮ Categorification of (induced) cell modules and the rough structure of generalised Verma modules ⋮ A GRAPHICAL DESCRIPTION OF (Dn,An−1) KAZHDAN–LUSZTIG POLYNOMIALS ⋮ Categorification of tensor product representations of \(\mathfrak{sl}_k\) and category \(\mathcal{O}\) ⋮ Translation and shuffling of projectively presentable modules and a categorification of a parabolic Hecke module ⋮ 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 \(G_{2}\) ⋮ A categorification of integral Specht modules ⋮ Symmetric structure for the endomorphism algebra of projective-injective module in parabolic category ⋮ Bigrassmannian permutations and Verma modules ⋮ Quadratic duals, Koszul dual functors, and applications ⋮ Parabolic category O, perverse sheaves on Grassmannians, Springer fibres and Khovanov homology ⋮ KOSTANT'S PROBLEM AND PARABOLIC SUBGROUPS ⋮ Representation type of the blocks of category \(\mathcal O_s\) ⋮ Twisted filtrations of Soergel bimodules and linear Rouquier complexes
Cites Work
- Weight filtrations for induced representations of real reductive Lie groups
- Moduln mit einem höchsten Gewicht
- Kazhdan-Lusztig conjecture and holonomic systems
- Models of representations of compact Lie groups
- On the relation between intersection cohomology and representation theory in positive characteristic.
- The combinatorics of Harish-Chandra bimodules.
- Kategorie O , Perverse Garben Und Moduln Uber Den Koinvariantez Zur Weylgruppe
- Koszul Duality Patterns in Representation Theory
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