Rank polynomials

Brandt, Marco, Dipper, Richard, James, Gordon and Lyle, Sinéad (2009) Rank polynomials. Proceedings of the London Mathematical Society, 98 (1). pp. 1-18. ISSN 0024-6115

Full text not available from this repository. (Request a copy)

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
Depositing User: Users 2731 not found.
Date Deposited: 14 Nov 2011 11:28
Last Modified: 21 Apr 2020 17:32
URI: https://ueaeprints.uea.ac.uk/id/eprint/35429
DOI: 10.1112/plms/pdn018

Actions (login required)

View Item View Item