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arXiv · 2009.06906

Enumeration of Gelfand-Cetlin type reduced words

Yunhyung Cho·Jang Soo Kim·Eunjeong Lee
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Abstract

The combinatorics of reduced words and commutation classes plays an important role in geometric representation theory. A string polytope is a lattice polytope associated to each reduced word of the longest element $w_0$ in the symmetric group which encodes the character of a certain irreducible representation of a Lie group of type $A$. In this paper, we provide a recursive formula for the number of reduced words of $w_0$ such that the corresponding string polytopes are combinatorially equivalent to a Gelfand-Cetlin polytope. The recursive formula involves the number of standard Young tableaux of shifted shape. We also show that each commutation class is completely determined by a list of quantities called indices.

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Yunhyung Cho, Jang Soo Kim, Eunjeong Lee. 2020-09-16. Enumeration of Gelfand-Cetlin type reduced words. https://arxiv.org/abs/2009.06906

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