Working Seminar on Representation Theory | |

Topic: | A Gelfand-Graev Formula and Stable Transfer Factors for $\mathrm{SL}_n$ |

Speaker: | Daniel Johnstone |

Affiliation: | University of Chicago |

Date: | Friday, January 27 |

Time/Room: | 2:00pm - 3:00pm/S-101 |

A result of Gelfand and Graev shows that the supercuspidal representations of $\mathrm{SL}_2$ are neatly parameterized by characters of elliptic tori, and that the stable character data for all such representations may be collected into a single function by means of a Fourier Transform. Using recent advances in the computation of characters of supercuspidal representations, we prove analogous results for the group $\mathrm{SL}_n$.