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

Ayyer, Arvind and Behrend, Roger E (2019) Factorization theorems for classical group characters, with applications to alternating sign matrices and plane partitions. In: JOURNAL OF COMBINATORIAL THEORY SERIES A, 165 . pp. 78-105.

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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) 14] 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. (C) 2019 Elsevier Inc. All rights reserved.

Item Type:	Journal Article
Publication:	JOURNAL OF COMBINATORIAL THEORY SERIES A
Publisher:	ACADEMIC PRESS INC ELSEVIER SCIENCE
Additional Information:	Copyright of this article belongs to ACADEMIC PRESS INC ELSEVIER SCIENCE.
Keywords:	Schur polynomials; Classical group characters; Alternating sign matrices; Plane partitions
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	24 May 2019 12:58
Last Modified:	24 May 2019 12:58
URI:	http://eprints.iisc.ac.in/id/eprint/62564

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