Graded $q$-Schur algebras

Abstract

Generalizing recent work of Brundan and Kleshchev, we introduce grading on Dipper-James' $q$-Schur algebra, and prove a graded analogue of the Leclerc and Thibon's conjecture on the decomposition numbers of the $q$-Schur algebra when $q^2\ne 1$ and $q^3\ne 1$.

25 pages, (v2) added details of the proof, (v3) have changed notations to standard ones and corrected various confusions

References in corpus (5)

• A diagrammatic approach to categorification of quantum groups I
• 2-Kac-Moody algebras
• Blocks of cyclotomic Hecke algebras and Khovanov-Lauda algebras
• Graded decomposition numbers for cyclotomic Hecke algebras
• Graded Specht modules

Cited by in corpus (8)

• Crystals from categorified quantum groups
• Quiver Schur algebras and q-Fock space
• Canonical bases and higher representation theory
• Categorifications from planar diagrammatics
• Universal Verma modules and the Misra-Miwa Fock space
• A semisimple series for $q$-Weyl and $q$-Specht modules
• Parallelotope tilings and $q$-decomposition numbers
• On a higher level extension of Leclerc-Thibon product theorem in q-deformed Fock spaces