Renner幺半群的一般Hecke代数
Generic Hecke algebra for Renner monoids
摘要：
每个Renner幺半群$R$都对应一个\emph{generic Hecke algebra} $\H(R)$ over $\mathbb{Z}[q]$，它是$R$的幺半群$\mathbb{Z}$ -代数的变形.如果$M$是一个有限的约化幺半群，其上有Borel子群$B$和相应的Renner幺半群$R$，那么我们通过在$\H(R)$中专门化$q$，并在$\mathbb{Z}$上用$\mathbb{C}$张量，得到相应的Iwahori-Hecke代数$\H(M,B)$，就像在有限代数群的经典情况下一样。这肯定地回答了L.所罗门
英文摘要：
We associate with every Renner monoid $R$ a \emph{generic Hecke algebra} $\H(R)$ over $\mathbb{Z}[q]$ which is a deformation of the monoid $\mathbb{Z}$-algebra of $R$. If $M$ is a finite reductive monoid with Borel subgroup $B$ and associated Renner monoid $R$, then we obtain the associated Iwahori-Hecke algebra $\H(M,B)$ by specialising $q$ in $\H(R)$ and tensoring by $\mathbb{C}$ over $\mathbb{Z}$, as in the classical case of finite algebraic groups. This answers positively to a long-standing question of L. Solomon.
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