Speaker: 吕恒飞，北京航空航天大学

Inviter: 聂思安研究员

Title: The Prasad-Takloo-Bighash conjecture

Language: Chinese

Time & Venue: 2024.11.28 14:30-15:30 数学院南楼N818

Abstract: Let E be a quadratic field extension over F. Let A be a central simple algebra over F containing E. Let B be the centralizer of E inside A. Then (GL(1,A),GL(1,B)) forms a symmetric pair, called the Prasad-Takloo-Bighash pair. Given a character \chi of E*, it will induce a character on GL(1,B), still denoted by \chi. In this talk, we will show that Hom(\pi,\chi) is at most 1-dimensional for certain irreducible representations of GL(1,A). Furthermore, we will show that \pi is \chi-self-dual. When E=F+F, we will show that \dim Hom(\pi,\chi) is at most 1 for any irreducible representation of GL(2n,F) and any character \chi of GL(n,F) x GL(n,F). This is a joint work with Nadir Matringe.