## Characters of Renner Monoids and Their Hecke Algebras. (arXiv:1811.12343v1 [math.RT])

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

## Solidot 文章翻译

 你的名字 留空匿名提交 你的Email或网站 用户可以联系你 标题 简单描述 内容 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.