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arXiv · 1007.0820

A plactic algebra of extremal weight crystals and the Cauchy identity for Schur operators

Jae-Hoon Kwon
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Abstract

We give a new bijective interpretation of the Cauchy identity for Schur operators which is a commutation relation between two formal power series with operator coefficients. We introduce a plactic algebra associated with the Kashiwara's extremal weight crystals over the Kac-Moody algebra of type $A_{+\infty}$, and construct a Knuth type correspondence preserving the plactic relations. This bijection yields the Cauchy identity for Schur operators as a homomorphic image of its associated identity for plactic characters of extremal weight crystals, and also recovers the Sagan and Stanley's correspondence for skew tableaux as its restriction.

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BibTeXRIS

Jae-Hoon Kwon. 2010-07-06. A plactic algebra of extremal weight crystals and the Cauchy identity for Schur operators. https://arxiv.org/abs/1007.0820

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