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arXiv · 1309.6917

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

Anton Evseev
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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.

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BibTeXRIS

Anton Evseev. 2013-09-26. On graded decomposition numbers for cyclotomic Hecke algebras in quantum characteristic 2. https://doi.org/10.1112/blms%2Fbdu028

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