论文标题
关于Gelfand-Graev表示的内态代数II
On endomorphism algebras of Gelfand-Graev representations II
论文作者
论文摘要
令$ g $为特征$ p $的有限字段$ \ mathbb {f} _q $定义的连接还原组，带有deligne-lusztig dual $ g^\ ast $。我们表明，超过$ \ overline {\ m马布{z}} [1/pm] $，其中$ m $是$ g $的所有不良数量的产物，$ g $，gelfand-graev-graev-graev表示$ g（\ mathbb {f} _q）$是Grothendieeck ringimention difime difor的ringiment of grothendieeck ringiment of grothendieeck。 $ edline {\ mathbb {f}} _ q $ - $ g^\ ast的列表（\ mathbb {f} _q）$。
Let $G$ be a connected reductive group defined over a finite field $\mathbb{F}_q$ of characteristic $p$, with Deligne--Lusztig dual $G^\ast$. We show that, over $\overline{\mathbb{Z}}[1/pM]$ where $M$ is the product of all bad primes for $G$, the endomorphism ring of a Gelfand--Graev representation of $G(\mathbb{F}_q)$ is isomorphic to the Grothendieck ring of the category of finite-dimensional $\overline{\mathbb{F}}_q$-representations of $G^\ast(\mathbb{F}_q)$.
