Kazhdan-Lusztig conjecture for affine Lie algebras with negative level

DOI10.1215/S0012-7094-95-07702-3zbMath0829.17020OpenAlexW1490233935MaRDI QIDQ1804678

Masaki Kashiwara, Toshiyuki Tanisaki

Publication date: 22 January 1996

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/s0012-7094-95-07702-3

zbMATH Keywords

Weyl group Cartan subalgebra affine Lie algebra Kazhdan-Lusztig polynomial

Mathematics Subject Classification ID

Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67) Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.) (22E47)

Related Items

Schubert calculus and torsion explosion, A conjectural extension of the Kazhdan-Lusztig equivalence, Graded decomposition matrices of 𝑣-Schur algebras via Jantzen filtration, The weights of simple modules in category \(\mathcal{O}\) for Kac-Moody algebras, Irreducible modules of quantized enveloping algebras at roots of 1, ii, BGG categories in prime characteristics, Infrared computations of defect Schur indices, Representation theory of \(\mathcal{W}\)-algebras, Quantum groups, the loop Grassmannian, and the Springer resolution, Coxeter combinatorics for sum formulas in the representation theory of algebraic groups, Row and column removal theorems for homomorphisms of Specht modules and Weyl modules., Semi-infinite Schubert varieties and quantum 𝐾-theory of flag manifolds, A Fock space model for decomposition numbers for quantum groups at roots of unity, Algebraic representations and constructible sheaves, Leray's quantization of projective duality, Irreducible modules of quantized enveloping algebras at roots of 1, Diagram categories for \(\mathrm{U}_q\)-tilting modules at roots of unity, LECTURES ON THE GEOMETRY AND MODULAR REPRESENTATION THEORY OF ALGEBRAIC GROUPS, A Weyl module stratification of integrable representations. With an appendix by Ryosuke Kodera, Cohomology in singular blocks of parabolic category, On the Satake isomorphism, Localization for affine \(\mathcal{W} \)-algebras, Differentiating the Weyl generic dimension formula with applications to support varieties, Dimensions of modular irreducible representations of semisimple Lie algebras, Working session: Geometric representation theory. Abstracts from the working session held April 3--9, 2022, An informal introduction to categorical representation theory and the local geometric Langlands program, Kazhdan-Lusztig combinatorics in the moment graph setting, Quantum groups at roots of ±1, Wall-Crossing functors and D-modules, Generic and \(q\)-rational representation theory, The Steinberg-Lusztig tensor product theorem, Casselman-Shalika, and LLT polynomials, Characteristic cycles for the loop Grassmannian and nilpotent orbits., On the decomposition matrices of the quantized Schur algebra, A new approach to the Koszul property in representation theory using graded subalgebras, Almost dominant generalized slices and convolution diagrams over them, The Weyl-Kac weight formula, Koszul duality of affine Kac-Moody algebras and cyclotomic rational double affine Hecke algebras, Pursuing the double affine Grassmannian. I: Transversal slices via instantons on \(A_k\)-singularities, Localization of \(\mathfrak g\)-modules on the affine Grassmannian, Induced and simple modules of double affine Hecke algebras., Hall algebras and quantum Frobenius, Cohomology in singular blocks for a quantum group at a root of unity, Integrable crystals and restriction to Levi subgroups via generalized slices in the affine Grassmannian, Reductive groups, the loop Grassmannian, and the Springer resolution, Sheaves on affine Schubert varieties, modular representations, and Lusztig’s conjecture, Kazhdan-Lusztig conjecture for affine Lie algebras with negative level. II: Nonintegral case, Highest weight modules for algebraic groups arising from quantum groups, Quantum Langlands duality of representations of -algebras, A simple character formula, Affine Beilinson-Bernstein localization at the critical level for \(\mathrm{GL}_2\), Some aspects of finite linear groups: A survey, On the stable moment graph of an affine Kac–Moody algebra, Light leaves and Lusztig's conjecture, Parabolic Kazhdan-Lusztig polynomials and Schubert varieties, Another realization of the category of modules over the small quantum group, Balanced semisimple filtrations for tilting modules, Some new examples in 1-cohomology

Cites Work