Graded decomposition numbers for cyclotomic Hecke algebras

Abstract

In recent joint work with Wang, we have constructed graded Specht modules for cyclotomic Hecke algebras. In this article, we prove a graded version of the Lascoux-Leclerc-Thibon conjecture, describing the decomposition numbers of graded Specht modules over a field of characteristic zero.

57 pages; final version

References in corpus (10)

• A diagrammatic approach to categorification of quantum groups I
• 2-Kac-Moody algebras
• Blocks of cyclotomic Hecke algebras and Khovanov-Lauda algebras
• Blocks of cyclotomic Hecke algebras
• Graded Specht modules
• Affine sl_p controls the representation theory of the symmetric group and related Hecke algebras
• Representations of shifted Yangians and finite W-algebras
• Canonical bases and Khovanov-Lauda algebras
• The degenerate analogue of Ariki's categorification theorem
• Highest weight categories arising from Khovanov's diagram algebra III: category O

Cited by in corpus (82)

• Blocks of cyclotomic Hecke algebras and Khovanov-Lauda algebras
• Categorification of Highest Weight Modules via Khovanov-Lauda-Rouquier Algebras
• Crystals from categorified quantum groups
• Graded Specht modules
• Quiver Schur algebras and q-Fock space
• Canonical bases and higher representation theory
• On category O for cyclotomic rational Cherednik algebras
• The sl_3 web algebra
• Categorifications from planar diagrammatics
• Affine Cellularity of Khovanov-Lauda-Rouquier algebras in type A
• Highest weight categories arising from Khovanov's diagram algebra III: category O
• Degenerate cyclotomic Hecke algebras and higher level Heisenberg categorification
• Graded $q$-Schur algebras
• Trace as an alternative decategorification functor
• An LLT-type algorithm for computing higher-level canonical bases
• The many graded cellular bases of Hecke algebras
• sl(N)-Web categories
• Heisenberg and Kac-Moody categorification
• Quiver Schur algebras for linear quivers
• Cyclotomic Yokonuma-Hecke algebras are cyclotomic quiver Hecke algebras
• Graded decomposition numbers for the blob algebra
• Specht modules for quiver Hecke algebras of type $C$
• ${\mathfrak{gl}}_n$-webs, categorification and Khovanov-Rozansky homologies
• Quiver Schur algebras and Koszul duality
• Indecomposable 1-morphisms of \dot{U}^+_3 and the canonical basis of U_q^+(sl_3)
• The sl(N)-web algebras and dual canonical bases
• Schurian-finiteness of blocks of type $A$ Hecke algebras
• Graded dimensions and monomial bases for the cyclotomic quiver Hecke algebras
• Tame block algebras of Hecke algebras of classical type
• Quiver Hecke algebras and 2-Lie algebras
• On the structure of cyclotomic nilHecke algebras
• Nilpotency in type A cyclotomic quotients
• Ozsvath-Szabo bordered algebras and subquotients of category O
• Cellularity and subdivision of KLR and weighted KLRW algebras
• On graded decomposition numbers for cyclotomic Hecke algebras in quantum characteristic 2
• Graded induction for Specht modules
• Cuspidal systems for affine Khovanov-Lauda-Rouquier algebras
• Categorification of highest weight modules over quantum generalized Kac-Moody algebras
• Skew cellularity of the Hecke algebras of type $G(\ell ,p,n)$
• Core blocks for Hecke algebras of type B and sign sequences
• The Khovanov-Lauda 2-category and categorifications of a level two quantum sl(n) representation
• Homomorphisms between standard modules over finite type KLR algebras
• Universal Verma modules and the Misra-Miwa Fock space
• Content systems and deformations of cyclotomic KLR algebras of type $A$ and $C$
• Factorization of the canonical bases for higher level Fock spaces
• Modular Representation Theory of Symmetric Groups
• Modular branching rules for projective representations of symmetric groups and lowering operators for the supergroup Q(n)
• On bases of some simple modules of symmetric groups and Hecke algebras
• On a generalization of Dipper--James--Murphy's Conjecture
• Representations of Khovanov-Lauda-Rouquier Algebras and Combinatorics of Lyndon Words
• Specht modules labelled by hook bipartitions I
• An equivalence between truncations of categorified quantum groups and Heisenberg categories
• Heisenberg algebra, wedges and crystals
• Blocks of the Brauer category over the complex field
• Branching graphs for finite unitary groups in non-defining characteristic
• Representation type of cyclotomic quiver Hecke algebras of type $A_{\ell }^{(1)}$
• Graded cellular bases for Temperley-Lieb algebras of type A and B
• Matrix units and Schur elements for the degenerate cyclotomic Hecke algebras
• Representations of weakly triangular categories
• Irreducible Specht modules for Iwahori-Hecke algebras of type B
• Decomposable Specht modules indexed by bihooks
• An analogue of row removal for diagrammatic Cherednik algebras
• DG-Enhanced Hecke and KLR Algebras
• A categorical equivalence between affine Yokonuma-Hecke algebras and some quiver Hecke algebras
• Categorification of the internal braid group action for quantum groups I: 2-functoriality
• Morita equivalences between cyclotomic KLR algebras in types ${\mathtt{C}}_{\infty }$ and ${\mathtt{A}}_{\infty }$
• Decomposable Specht modules indexed by bihooks II
• Representations of cyclotomic oriented Brauer categories
• Strands algebras and the affine highest weight property for equivariant hypertoric categories
• Young walls and graded dimension formulas for finite quiver Hecke algebras of type $A_{2\ell }^{(2)}$ and $D_{\ell +1}^{(2)}$
• Enhanced nilHecke algebras and baby Verma modules
• Cellularity of KLR and weighted KLRW algebras via crystals
• Representation type of higher level cyclotomic quiver Hecke algebras in affine type C
• Wild blocks of type $A$ Hecke algebras are strictly wild
• Empty runner removal theorem for Ariki-Koike algebras
• Induction and restriction on representations of dihedral groups
• Parallelotope tilings and $q$-decomposition numbers
• Trace and categorical sl(n) representations
• Combinatorics for graded Cartan matrices of the Iwahori-Hecke algebra of type A
• Representation Theory of Symmetric Groups and Related Hecke Algebras
• sl_2-actions along short strings for spin blocks
• An interpretation of the Lascoux-Leclerc-Thibon algorithm and graded representation theory