Title: Representations and Coefficient Systems on Buildings.
Speaker: Navarro Javier（Sorbonne Université, Paris）
Time: 1.23 (Friday), 16:00-17:00
Venue: zoom会议号: 943 3835 4802 密码: 0123
Link: https://zoom.us/j/94338354802?pwd=27f9ARN6b2bPbCZULPa79lvVscTqdb.1
Abstract: Representations of p-adic reductive groups are often studied in two complementary ways: by restricting to parabolic subgroups and by restricting to open compact subgroups. Each approach has a geometric avatar, namely the spherical building, which organizes the parabolic subgroups, and the Bruhat-Tits building, which records some compact open subgroups and guides the theory of types. In this talk, I will briefly introduce both buildings and explain how coefficient systems on them link geometry to representation theory. On the spherical side, one recovers familiar structures via induction and Jacquet modules. On the Bruhat-Tits side, after a quick tour of the Schneider-Stuhler construction and its refinement by Broussous-Schneider, I will present a recent result for GL(N) that confirms the expected acyclicity of the associated chain complex. I will then outline a generalization to other groups and indicate consequences for character computations.
