Minuscule representations and Panyushev conjectures

被引：0
|
作者：
Chaoping Dong
Guobiao Weng
机构：
[1] Hunan University,Institute of Mathematics
[2] Dalian University of Technology,School of Mathematical Sciences
来源：
Science China Mathematics | 2018年 / 61卷
关键词：
minuscule poset; -polynomial; -polynomial; ℤ-gradings of Lie algebra; 06A07; 17B10;
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摘要：
Recently, Panyushev (2015) raised five conjectures concerning the structure of certain root posets arising from Z-gradings of simple Lie algebras. This paper aims to provide proofs for four of them. Our study also links these posets with Kostant-Macdonald identity, minuscule representations, Stembridge’s “t = −1 phenomenon”, and the cyclic sieving phenomenon due to Reiner et al. (2004).
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页码：1759 / 1774
页数：15
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