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Indexed by:期刊论文

Date of Publication:2018-10-01

Journal:SCIENCE CHINA-MATHEMATICS

Included Journals:SCIE

Volume:61

Issue:10

Page Number:1759-1774

ISSN No.:1674-7283

Key Words:minuscule poset; M-polynomial; N-polynomial; Z-gradings of Lie algebra

Abstract: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).