Factorization theorems for classical group characters, with applications to alternating sign matrices and plane partitions

Ayyer, Arvind and Behrend, Roger E. ORCID: https://orcid.org/0000-0002-6143-7439 2019. Factorization theorems for classical group characters, with applications to alternating sign matrices and plane partitions. Journal of Combinatorial Theory, Series A 165 , pp. 78-105. 10.1016/j.jcta.2019.01.001

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Abstract

We show that, for a certain class of partitions and an even number of variables of which half are reciprocals of the other half, Schur polynomials can be factorized into products of odd and even orthogonal characters. We also obtain related factorizations involving sums of two Schur polynomials, and certain odd-sized sets of variables. Our results generalize the factorization identities proved by Ciucu and Krattenthaler (2009) for partitions of rectangular shape. We observe that if, in some of the results, the partitions are taken to have rectangular or double-staircase shapes and all of the variables are set to 1, then factorization identities for numbers of certain plane partitions, alternating sign matrices and related combinatorial objects are obtained.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Uncontrolled Keywords:	Schur polynomials, classical group characters, alternating sign matrices, plane partitions
Publisher:	Elsevier
ISSN:	0097-3165
Date of First Compliant Deposit:	2 May 2018
Date of Acceptance:	28 December 2018
Last Modified:	29 Nov 2024 09:45
URI:	https://orca.cardiff.ac.uk/id/eprint/110908

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