On graded decomposition numbers for cyclotomic Hecke algebras in quantum characteristic 2

Abstract

Brundan and Kleshchev introduced graded decomposition numbers for representations of cyclotomic Hecke algebras of type $A$, which include group algebras of symmetric groups. Graded decomposition numbers are certain Laurent polynomials, whose values at 1 are the usual decomposition numbers. We show that in quantum characteristic 2 every such polynomial has non-zero coefficients either only in odd or only in even degrees. As a consequence, we find the first examples of graded decomposition numbers of symmetric groups with non-zero coefficients in some negative degrees.

6 pages. Definition of parity function $\epsilon$ corrected for $l>1$. Comments welcome. To appear in Bulletin of the London Mathematical Society

References in corpus (4)

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

Cited by in corpus (2)

• Content systems and deformations of cyclotomic KLR algebras of type $A$ and $C$
• Graded decomposition numbers of Ariki-Koike algebras for blocks of small weight