researchseminars.org

Peter Gräf (BU)
2022-05-02 20:15 - 21:15 UTC | https://researchseminars.org/talk/BUNT/12/
Title: A residue map and a Poisson kernel for $GL_3$ (https://researchseminars.org/talk/BUNT/12/)
by Peter Gräf (BU) as part of Boston University Number Theory Seminar

Abstract
In the classical theory of modular and automorphic forms it has proven to be very useful to realize spaces of such forms in more combinatorial or algebraic ways. A famous instance of such a realization is the relationship between classical modular forms and modular symbols. In this talk, I will discuss a non-archimedean analogue of this construction, namely the relationship between certain holomorphic discrete series representations on the Drinfeld period domain and spaces of harmonic cocycles on the Bruhat-Tits building for the group $GL_3$ over a non-archimedean local field of any characteristic. The main novelty is that we allow non-trivial coefficients in a situation beyond the well-known theory for $GL_2$, which extends works of Schneider and Teitelbaum. I will explain how to construct a residue map and a Poisson kernel in this situation. Moreover, I will explain how the existence of the relevant boundary distributions follows from a conjectural non-criticality statement for certain (generalized) automorphic forms.
