Rank polynomials

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

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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
UEA Research Groups: Faculty of Science > Research Groups > Algebra and Combinatorics
Depositing User: Users 2731 not found.
Date Deposited: 14 Nov 2011 11:28
Last Modified: 08 Jan 2024 01:20
URI: https://ueaeprints.uea.ac.uk/id/eprint/35429
DOI: 10.1112/plms/pdn018

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