For more information about this meeting, contact Karl Schwede, Robert Vaughan, Mihran Papikian, Ae Ja Yee.

Title: | Topics in the representation theory of SL(2) |

Seminar: | Algebra and Number Theory Seminar |

Speaker: | Roger Plymen, University of Manchester |

Abstract Link: | http://www.math.psu.edu/schwede/Plymen_abstract_PSU_2013.pdf |

Abstract: |

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. |

### Room Reservation Information

Room Number: | MB106 |

Date: | 10 / 03 / 2013 |

Time: | 11:15am - 12:05pm |