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 |
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Faculty \ School: | Faculty of Science > School of Mathematics (former - to 2024) |
UEA Research Groups: | Faculty of Science > Research Groups > Algebra and Combinatorics |
Depositing User: | Pure Connector |
Date Deposited: | 15 Dec 2016 00:06 |
Last Modified: | 31 Aug 2024 00:36 |
URI: | https://ueaeprints.uea.ac.uk/id/eprint/61738 |
DOI: | 10.1007/s00031-017-9444-7 |
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