Informal Friday Seminar: Baine -- Representations of SL_2(F_q)

The complex representations of SL_2(F_q) have been understood since Schur’s work in
1907.  However, Schur’s approach relied upon many ’ad hoc’ methods.  In 1974
Drinfeld constructed a Langlands correspondence for GL_2(K), where K is a global
field of equal characteristic, and showed in the course of this work that the cuspidal
characters of SL_2(F_q) can be found in the first l-adic cohomology group of the
Drinfeld Curve.  This approach was generalised by Deligne and Lusztig, establishing
Deligne-Lusztig Theory.  In this two-part talk, we will cover how the complex cuspidal
representations of SL_2(F_q) can be realised in the first l-adic cohomology group of
the Drinfeld Curve.  Part one will focus on preliminary material relating to the group
SL_2(F_q) and the geometry of the Drinfeld Curve.  Part two will focus on the
representation theory of SL_2(F_q).  These talks are intended to supplement Geordie’s
Langlands correspondence series.

**Note that the IFS has changed its meeting time**