GALOIS REPRESENTATIONS AND AUTOMORPHIC FORMS SEMINAR | |

Topic: | The Bernstein Center of the Category of Smooth W(k)[GL_n(F)]-Modules |

Speaker: | David Helm |

Affiliation: | University of Texas |

Date: | Thursday, April 14 |

Time/Room: | 2:15pm - 3:15pm/S-101 |

Video Link: | https://video.ias.edu/galois/helm |

The Bernstein center plays a role in the representation theory of locally profinite groups analogous to that played by the center of the group ring in the representation theory of finite groups. When F is a finite extension of Q_p, we discuss the Bernstein center of the category of smooth representations of GL_n(F) over the Witt vectors of an algebraically closed field of characteristic l not equal to p. We will prove results on the basic structure of the Bernstein center, and describe a conjecture that has implications for the local Langlands correspondence in algebraic families.