Let $E$ be the endomorphism algebra of a Gelfand-Graev representation over integral coefficients of the finite reductive group $G^F$ ($G$ is a connected reductive group defined over $F_q$ with the induced Frobenius endomorphism F). Recent developments of local Langlands program suggest that $E$ may be described by the ring of functions $B$ of the $\mathbb{Z}$-scheme $({T^{\vee}}//W)^{F^\vee}$ (Langlands dual side). Such a description of $E$ by $B$ is however a problem in the level of finite groups, and an approach to this description without p-adic techniques from local Langlands is expected. In this talk we will give, under some additional hypotheses, a such approach by comparing both $E$ and $B$ with the Grothendieck group $K$ of the category of representations of ${G^*}^{F^*}$ (Deligne-Lusztig dual side) over defining characteristic.

★ Visitors need to show the gate guard NTU Visitor Pass to enter the campus. Please fill the following form to apply for 1-Day Pass.
★ Registration deadline: 3PM, Oct. 5
Registration form