The University of Southampton
University of Southampton Institutional Repository

# Extended Bressoud-Wei and Koike skew Schur function identities

Hamel, A.M. and King, R.C. (2011) Extended Bressoud-Wei and Koike skew Schur function identities Journal of Combinatorial Theory, Series A, 118, (2), pp. 545-557.

Record type: Article

## Abstract

The Jacobi-Trudi identity expresses a skew Schur function as a determinant of complete symmetric functions. Bressoud and Wei extend this idea, introducing an integer parameter $t\geq-1$ and showing that signed sums of skew Schur functions of a certain shape are expressible once again as a determinant of complete symmetric functions. Koike provides a Jacobi-Trudi-style definition of universal rational characters of the general linear group and gives their expansion as a signed sum of products of Schur functions in two distinct sets of variables. Here we extend Bressoud and Wei's formula by including an additional parameter and extending the result to the case of all integer $t$. Then we introduce this parameter idea to the Koike formula, extending it in the same way. We prove our results algebraically using Laplace determinantal expansions.

Full text not available from this repository.

Published date: 15 May 2011
Keywords: schur functions, jacobi–trudi identity, weyl identities
Organisations: Applied Mathematics

## Identifiers

Local EPrints ID: 195341
URI: http://eprints.soton.ac.uk/id/eprint/195341
ISSN: 0097-3165
PURE UUID: 7de18887-3277-4379-be71-c0b2dc330000

## Catalogue record

Date deposited: 30 Sep 2011 08:37

## Contributors

Author: A.M. Hamel
Author: R.C. King

## University divisions

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×