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Extended Bressoud-Wei and Koike skew Schur function identities

Record type: Article

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.

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Citation

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. (doi:10.1016/j.jcta.2010.05.002).

More information

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
Last modified: 18 Jul 2017 11:25

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Contributors

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

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