The p-canonical basis for Hecke algebras

DOI10.1090/conm/683/13719zbMath1390.20001arXiv1510.01556OpenAlexW2220001513MaRDI QIDQ2979688

Lars Thorge Jensen, Geordie Williamson

Publication date: 26 April 2017

Published in: Categorification and Higher Representation Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1510.01556

zbMATH Keywords

Weyl groupGrassmannianHecke algebrasemi-simple algebraic groupcanonical basistilting moduleCoxeter systemroot datumLanglands dual group

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Hecke algebras and their representations (20C08) Modular representations and characters (20C20) Reflection and Coxeter groups (group-theoretic aspects) (20F55) Grassmannians, Schubert varieties, flag manifolds (14M15)

Related Items (23)

Schubert calculus and torsion explosion ⋮ \((\ell, p)\)-Jones-Wenzl idempotents ⋮ The anti-spherical category ⋮ Categorification via blocks of modular representations for ⋮ Algebraic representations and constructible sheaves ⋮ Hecke action on the principal block ⋮ Calculating the \(p\)-canonical basis of Hecke algebras ⋮ \(\mathrm{SL}_2\) tilting modules in the mixed case ⋮ Working session: Geometric representation theory. Abstracts from the working session held April 3--9, 2022 ⋮ IntroSurvey of representation theory ⋮ Web calculus and tilting modules in type \(C_2\) ⋮ Billiards and tilting characters for \(\mathrm{SL}_3\) ⋮ The ABC of \(p\)-cells ⋮ Blob algebra and two-color Soergel calculus ⋮ Reductive groups, the loop Grassmannian, and the Springer resolution ⋮ Mixed Perverse Sheaves on Flag Varieties for Coxeter Groups ⋮ Koszul duality for Kac–Moody groups and characters of tilting modules ⋮ Jucys-Murphy elements for Soergel bimodules ⋮ \(p\)-Jones-Wenzl idempotents ⋮ A simple character formula ⋮ On the Humphreys conjecture on support varieties of tilting modules ⋮ The modular Weyl-Kac character formula ⋮ Smith-Treumann theory and the linkage principle

Cites Work

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• Parity sheaves on the affine Grassmannian and the Mirković-Vilonen conjecture
• Characteristic cycles and decomposition numbers
• Canonical basis, KLR algebras and parity sheaves
• The Hodge theory of Soergel bimodules.
• Parity sheaves, moment graphs and the \(p\)-smooth locus of Schubert varieties
• Diagrammatics for Soergel categories
• Decomposition theorem for proper Kähler morphisms
• On the Soergel bimodule category.
• Presentation of right-angled Soergel categories by generators and relations.
• La conjecture de Weil. II
• Representations of Coxeter groups and Hecke algebras
• On tilting modules for algebraic groups
• Equivariant sheaves and functors
• Geometric construction of crystal bases
• On the decomposition numbers of the Hecke algebra of \(G(m,1,n)\)
• On the relation between intersection cohomology and representation theory in positive characteristic.
• Exotic tilting sheaves, parity sheaves on affine Grassmannians, and the Mirković-Vilonen conjecture
• Kac-Moody groups, their flag varieties and representation theory
• Hecke algebras at roots of unity and crystal bases of quantum affine algebras
• Modular intersection cohomology complexes on flag varieties
• Light leaves and Lusztig's conjecture
• Diagrammatics for Coxeter groups and their braid groups
• Geometric Langlands duality and representations of algebraic groups over commutative rings
• Schémas en groupes. III: Structure des schémas en groupes réductifs. Exposés XIX à XXVI. Séminaire de Géométrie Algébrique du Bois Marie 1962/64 (SGA 3), dirigé par Michel Demazure et Alexander Grothendieck. Revised reprint
• On Ringel duality for Schur algebras
• The two-color Soergel calculus
• Parity sheaves and tilting modules
• Modular perverse sheaves on flag varieties I: tilting and parity sheaves
• A reducible characteristic variety in type A
• Quiver Hecke Algebras and 2-Lie Algebras
• Parity sheaves
• Affine Springer Fibers and Affine Deligne-Lusztig Varieties
• Canonical bases and KLR-algebras
• The decomposition theorem, perverse sheaves and the topology of algebraic maps
• Kazhdan-Lusztig-Polynome und eine Kombinatorik für Kipp-Moduln
• Soergel Calculus and Schubert Calculus
• Tilting modules and the p-canonical basis
• The Decomposition Matrices of GL _n (q ) for n ⩽ 10
• Schubert calculus and torsion explosion
• KAZHDAN-LUSZTIG-POLYNOME UND UNZERLEGBARE BIMODULN ÜBER POLYNOMRINGEN
• Soergel calculus
• Decomposition of tensor products of modular irreducibles for SL2
• Linear algebraic groups.

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