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 -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 " 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