Drinfeld curves and geometric Mackey Formula
This blog serves as my preparation for my talk at Bloch's seminar workshop on Deligne-Lusztig varieties. I will present a talk about $\ell$-adic cohomology of Drinfeld curves, which are easiest examples of Degline-Lusztig varieties. To begin with, the story dates back to representation theory of finite group of Lie type (by a finite group of Lie type, I mean $G^F$ with $G$ a reductive group over a finite field and $F$ the Frobenious endomorphism). To say why these groups are important, it is the classification of finite simple groups saying that any finite simplegroup belongs to four classes: cyclic, alternating, $26$ sporadic groups, and the others are all of Lie type. The central object of this blog is $SL_2(\mathbb{F}_q)$ with $q=p^r$ a prime power. It is a finite group of Lie type whose cardinality is $q(q-1)(q+1)$ (it's a fun exercise to show this in case you do not know). Not only $SL_2(\mathbb{F}_q)$, but the representation theory of any finite group over complex numbe...