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Description: | Number Theory Seminar Speaker: Vincent Sécherre, Université de Versailles Saint-Quentin Date & Time: Tuesday, January 30, 14:30-15:30. Venue: Ramanujan Hall Title: Supercuspidal representations of GL(n,K) distinguished by GL(n,F), with K/F a quadratic extension of p-adic fields. Abstract: Let p be an odd prime number and K/F be a quadratic extension of p-adic fields. Say that an irreducible representation of GL(n,K) is distinguished by GL(n,F) if its vector space carries a GL(n,F)-invariant nonzero linear form. Any distinguished representation is isomorphic to the contragredient of its Gal(K/F)-conjugate, but the converse is not true. We will explain how to canonically associate to any Gal(K/F)-selfcontragredient supercuspidal representation of GL(n,K) a finite tamely ramified extension T of F and a character of the multiplicative group of T, by using Bushnell-Kutzko’s theory of types, and how to get a necessary and sufficient condition on this character for this supercuspidal representation to be distinguished. |

Location: | Ramanujan Hall |

Date: | Tuesday, January 30, 2018 |

Time: | 2:30pm-3:30pm IST |

Duration: | 1 hour |

Access: | Public |