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Brandt, Marco, Dipper, Richard, James, Gordon and Lyle, Sinéad 
ORCID: https://orcid.org/0000-0002-6032-7721
(2009)
Rank polynomials.
Proceedings of the London Mathematical Society, 98 (1).
pp. 1-18.
ISSN 0024-6115
Abstract
A long-standing open problem in the representation theory of the finite general linear groups is to determine a ‘standard basis’ for the Specht modules. Such a basis would be analogous to the most commonly used basis for the Specht modules of the symmetric groups which is indexed by standard tableaux of a given shape. Here we show the existence of such a basis when the Specht module is indexed by a partition with two parts. In order to prove the result, we introduce a class of polynomials which we call rank polynomials; the combinatorics of these rank polynomials turns out to be intriguing in its own right.
| 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: | Users 2731 not found. |
| Date Deposited: | 14 Nov 2011 11:28 |
| Last Modified: | 07 Nov 2024 12:33 |
| URI: | https://ueaeprints.uea.ac.uk/id/eprint/35429 |
| DOI: | 10.1112/plms/pdn018 |
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