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arXiv · 1511.02692

Minuscule representations and Panyushev conjectures

Chao-Ping Dong·Guobiao Weng
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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.

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BibTeXRIS

Chao-Ping Dong, Guobiao Weng. 2015-11-09. Minuscule representations and Panyushev conjectures. https://doi.org/10.1007/s11425-017-9136-y

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