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), 545-557. (doi:10.1016/j.jcta.2010.05.002).

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Description/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.

Item Type: Article
ISSNs: 0097-3165 (print)
1096-0899 (electronic)
Keywords: schur functions, jacobi–trudi identity, weyl identities
Subjects: Q Science > QA Mathematics
Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Q Science > QA Mathematics > QA76 Computer software
Divisions: Faculty of Social and Human Sciences > Mathematical Sciences > Applied Mathematics
ePrint ID: 195341
Date Deposited: 30 Sep 2011 08:37
Last Modified: 27 Mar 2014 19:45
URI: http://eprints.soton.ac.uk/id/eprint/195341

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