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SUMMARY:Peter Gräf (BU)
DTSTART:20220502T201500Z
DTEND:20220502T211500Z
DTSTAMP:20260423T024659Z
UID:BUNT/12
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/BUNT/12/">A 
 residue map and a Poisson kernel for $GL_3$</a>\nby Peter Gräf (BU) as pa
 rt of Boston University Number Theory Seminar\n\n\nAbstract\nIn the classi
 cal theory of modular and automorphic forms it has proven to be very usefu
 l to realize spaces of such forms in more combinatorial or algebraic ways.
  A famous instance of such a realization is the relationship between class
 ical modular forms and modular symbols. In this talk\, I will discuss a no
 n-archimedean analogue of this construction\, namely the relationship betw
 een certain holomorphic discrete series representations on the Drinfeld pe
 riod domain and spaces of harmonic cocycles on the Bruhat-Tits building fo
 r the group $GL_3$ over a non-archimedean local field of any characteristi
 c. The main novelty is that we allow non-trivial coefficients in a situati
 on beyond the well-known theory for $GL_2$\, which extends works of Schnei
 der and Teitelbaum. I will explain how to construct a residue map and a Po
 isson kernel in this situation. Moreover\, I will explain how the existenc
 e of the relevant boundary distributions follows from a conjectural non-cr
 iticality statement for certain (generalized) automorphic forms.\n
LOCATION:https://researchseminars.org/talk/BUNT/12/
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