Graded decomposition matrices of 𝑣-Schur algebras via Jantzen filtration

DOI10.1090/S1088-4165-2012-00416-2zbMath1284.20050arXiv1006.1545OpenAlexW2963645461MaRDI QIDQ2889350

Peng Shan

Publication date: 7 June 2012

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

Full work available at URL: https://arxiv.org/abs/1006.1545

zbMATH Keywords

Weyl modulesJantzen filtrationparabolic Kazhdan-Lusztig polynomials\(v\)-Schur algebrasgraded decomposition matrices

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Representation theory for linear algebraic groups (20G05) Modular representations and characters (20C20) Schur and (q)-Schur algebras (20G43)

Related Items

A Fock space model for decomposition numbers for quantum groups at roots of unity, Positive Jantzen sum formulas for cyclotomic Hecke algebras, Quiver Schur algebras and Koszul duality., Universal Verma modules and the Misra-Miwa Fock space, ROUQUIER’S CONJECTURE AND DIAGRAMMATIC ALGEBRA, Schurian‐finiteness of blocks of type A$A$ Hecke algebras, Jantzen filtration of Weyl modules, product of Young symmetrizers and denominator of Young’s seminormal basis, The Steinberg-Lusztig tensor product theorem, Casselman-Shalika, and LLT polynomials, Rational parking functions and LLT polynomials, Character formulas and Bernstein–Gelfand–Gelfand resolutions for Cherednik algebra modules

Cites Work

• Universal Verma modules and the Misra-Miwa Fock space
• Double affine Hecke algebras, conformal coinvariants and Kostka polynomials
• \(D\)-modules, perverse sheaves, and representation theory. Translated from the Japanese by Kiyoshi Takeuchi
• Moduln mit einem höchsten Gewicht
• Projective modules over graded Lie algebras. I
• Structure of some categories of representations of infinite-dimensional Lie algebras
• Toward proof of Lusztig's conjecture concerning negative level representations of affine Lie algebras
• Centers and translation functors for the category \({\mathcal O}\) over Kac-Moody algebras
• On the category \(\mathcal O\) for rational Cherednik algebras.
• Parabolic Kazhdan-Lusztig polynomials and Schubert varieties
• \(D\)-modules on the affine Grassmannian and representations of affine Kac-Moody algebras
• Vertex algebras and the formal loop space
• Kazhdan-Lusztig conjecture for affine Lie algebras with negative level
• Decomposition numbers and canonical bases
• Kac-Moody groups, their flag varieties and representation theory
• The strong linkage principle for quantum groups at roots of 1.
• On the decomposition matrices of the quantized Schur algebra
• Cyclotomic double affine Hecke algebras and affine parabolic category \(\mathcal O\).
• Tensor Structures Arising from Affine Lie Algebras. I
• Parabolic category O, perverse sheaves on Grassmannians, Springer fibres and Khovanov homology
• Equivariant Derived Category and Representation of Real Semisimple Lie Groups
• Character formulas for tilting modules over Kac-Moody algebras
• Wall-Crossing functors and D-modules
• A q -Analogue of the Jantzen-Schaper Theorem
• Koszul Duality Patterns in Representation Theory
• Mixed Hodge modules
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item