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

de Boeck, Melanie, Evseev, Anton, Lyle, Sinead ORCID: https://orcid.org/0000-0002-6032-7721 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, Logic & Number Theory
Depositing User:	Pure Connector
Date Deposited:	15 Dec 2016 00:06
Last Modified:	07 Nov 2024 12:39
URI:	https://ueaeprints.uea.ac.uk/id/eprint/61738
DOI:	10.1007/s00031-017-9444-7

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