English

Minuscule representations and Panyushev conjectures

Representation Theory 2018-10-16 v9

Abstract

Recently, Panyushev raised five conjectures concerning the structure of certain root posets arising from Z\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=1t=-1 phenomenon", and the cyclic sieving phenomenon due to Reiner, Stanton and White.

Cite

@article{arxiv.1511.02692,
  title  = {Minuscule representations and Panyushev conjectures},
  author = {Chao-Ping Dong and Guobiao Weng},
  journal= {arXiv preprint arXiv:1511.02692},
  year   = {2018}
}

Comments

The paper has been accepted by SCIENCE CHINA Mathematics

R2 v1 2026-06-22T11:40:30.685Z