On bases of some simple modules of symmetric groups and Hecke algebras

Melanie de Boeck, Anton Evseev, Sinead Lyle, Liron Speyer

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Abstract

We consider simple modules for a Hecke algebra with a parameter of quantum characteristic e. Equivalently, we consider simple modules Dλ, labelled by e-restricted partitions λ of n, for a cyclotomic KLR algebra RΛ0nRnΛ0 over a field of characteristic p ≥ 0, with mild restrictions on p. If all parts of λ are at most 2, we identify a set DStde,p(λ) of standard λ-tableaux, which is defined combinatorially and naturally labels a basis of Dλ. In particular, we prove that the q-character of Dλ can be described in terms of DStde,p(λ). We show that a certain natural approach to constructing a basis of an arbitrary Dλ does not work in general, giving a counterexample to a conjecture of Mathas.
Original languageEnglish
Pages (from-to)631–669
Number of pages39
JournalTransformation Groups
Volume23
Issue number3
Early online date19 Oct 2017
DOIs
Publication statusPublished - Sep 2018

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