# Meeting Details

Title: Topics in the representation theory of SL(2) Algebra and Number Theory Seminar Roger Plymen, University of Manchester http://www.math.psu.edu/schwede/Plymen_abstract_PSU_2013.pdf We will focus on some topics in the representation theory of $G = SL_2(F)$. Here, $F$ will be a $p$-adic field such as $\Q_p$ or the local function field $\F_q((t))$. In the context of the local Langlands correspondence for $SL_2(F)$, there is a Langlands parameter $\varphi$ whose image in the dual group $PSL_2(\C)$ is the non-cyclic group of order $4$. This parameter $\varphi$ parameterizes $4$ irreducible complex representations of $G$. To describe these, we need to delve into the representation theory of $SL_2(\F_p)$. To separate the representations we need to enhance $\varphi$ in a certain way. We will also dip into the famous paper of Andr\'e Weil called \emph{Exercises dyadiques}. \medskip The talk will hopefully be self-contained, and I will try to develop things from first principles.