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Journal Articles Journal of Pure and Applied Algebra Year : 2017

On the one dimensional representations of Ariki-Koike algebras at roots of unity

Abstract

We study the natural labeling of the one dimensional representations for Ariki-Koike algebras at roots of unity. For Hecke algebras of types A and B, some of these representations can be identified with the socle of the Steinberg representation of a finite reductive group. We here give closed formulas for them. This uses, in particular, several results concerning crystal isomorphisms and the Mullineux involution.
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Dates and versions

hal-01197065 , version 1 (11-09-2015)

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Nicolas Jacon. On the one dimensional representations of Ariki-Koike algebras at roots of unity. Journal of Pure and Applied Algebra, 2017, 21 (7), ⟨10.1016/j.jpaa.2016.09.012⟩. ⟨hal-01197065⟩
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