Minuscule representations and Panyushev conjectures

Abstract

Recently, Panyushev raised five conjectures concerning the structure of certain root posets arising from $\mathbb{Z}$-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, Stanton and White.

The paper has been accepted by SCIENCE CHINA Mathematics

References in corpus (1)

• On Orbits of Order Ideals of Minuscule Posets

Cited by in corpus (1)

• Antichain generating polynomials of posets