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

de Boeck, Melanie, Evseev, Anton, Lyle, Sinead and Speyer, Liron (2018) On bases of some simple modules of symmetric groups and Hecke algebras. Transformation Groups, 23 (3). 631–669. ISSN 1083-4362

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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.

Item Type:	Article
Faculty \ School:	Faculty of Science > School of Mathematics (former - to 2024)
UEA Research Groups:	Faculty of Science > Research Groups > Algebra and Combinatorics (former - to 2024) Faculty of Science > Research Groups > Algebra, Number Theory, Logic, and Representations (ANTLR)
Depositing User:	Pure Connector
Date Deposited:	15 Dec 2016 00:06
Last Modified:	28 Mar 2025 07:54
URI:	https://ueaeprints.uea.ac.uk/id/eprint/61738
DOI:	10.1007/s00031-017-9444-7

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