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Abstract |
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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. |