Type: Seminar

Distribution: World

CalTitle1: Baine - Representations of SL_2(F_q)

Auth: romanova@dora.maths.usyd.edu.au

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**