A new concept of the X-M-PN space is introduced, and the acute angle principle in the X-M-PN space is proved. Meanwhile, some new results are obtained.
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 link...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).展开更多
文摘A new concept of the X-M-PN space is introduced, and the acute angle principle in the X-M-PN space is proved. Meanwhile, some new results are obtained.
基金supported by National Natural Science Foundation of China(Grant No.11571097)
文摘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).
