Release Time:2019-03-12  Hits:

Indexed by: Journal Article

Date of Publication: 2018-10-01

Journal: SCIENCE CHINA-MATHEMATICS

Included Journals: SCIE

Volume: 61

Issue: 10

Page Number: 1759-1774

ISSN: 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).