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Characters of Renner Monoids and Their Hecke Algebras. (arXiv:1811.12343v1 [math.RT])
来源于:arXiv
We explore the representation theory of Renner monoids associated to
classical groups and their Hecke algebras. In Cartan type $A_n$, the Hecke
algebra is a natural deformation of the rook monoid algebra, and its
representation theory has been studied extensively by Solomon and Halverson,
among others. It is known that the character tables are block upper triangular,
i.e. $M=AY=YB$ for some matrices $A$ and $B$. We compute the $A$ and $B$
matrices in Cartan type $B_n$ by using the results of Li, Li, and Cao to pursue
analogous results to those of Solomon. We then compute some type $B_n$ Hecke
algebra character values by using the same $B$ matrix as in the monoid case. 查看全文>>