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Lee, Eun Jeong
기하학 수리물리 연구단
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Enumeration of Gelfand-Cetlin type reduced words

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Title
Enumeration of Gelfand-Cetlin type reduced words
Author(s)
Cho, Yunhyung; Kim, Jang Soo; Eunjeong Lee
Publication Date
2022-02
Journal
ELECTRONIC JOURNAL OF COMBINATORICS, v.29, no.1
Publisher
ELECTRONIC JOURNAL OF COMBINATORICS
Abstract
The combinatorics of reduced words and their commutation classes plays an important role in geometric representation theory. For a semisimple complex Lie group G, a string polytope is a convex polytope associated with each reduced word of the longest element w0 in the Weyl group of G encoding the character of a certain irreducible representation of G. In this paper, we deal with the case of type A, i.e., G = SLn+1(C). A Gelfand-Cetlin polytope is one of the most famous examples of string polytopes of type A. We provide a recursive formula enumerating reduced words of w0 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.
URI
https://pr.ibs.re.kr/handle/8788114/12216
DOI
10.37236/10071
ISSN
1077-8926
Appears in Collections:
Center for Geometry and Physics(기하학 수리물리 연구단) > 1. Journal Papers (저널논문)
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