A short combinatorial proof of dimension identities of Erickson and Hunziker

Kumari, N (2024) A short combinatorial proof of dimension identities of Erickson and Hunziker. In: Journal of Combinatorial Theory. Series A, 205 .

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Abstract

In a recent paper (arXiv:2301.09744), Erickson and Hunziker consider partitions in which the arm�leg difference is an arbitrary constant m. In previous works, these partitions are called (�m)-asymmetric partitions. Regarding these partitions and their conjugates as highest weights, they prove an identity yielding an infinite family of dimension equalities between gln and gln+m modules. Their proof proceeds by the manipulations of the hook content formula. We give a simple combinatorial proof of their result. © 2024 Elsevier Inc.

Item Type:	Journal Article
Publication:	Journal of Combinatorial Theory. Series A
Publisher:	Academic Press Inc.
Additional Information:	The copyright for this article belongs to the Academic Press Inc.
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	24 Apr 2024 05:54
Last Modified:	24 Apr 2024 05:54
URI:	https://eprints.iisc.ac.in/id/eprint/84603

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