Representations of GL_2 over Z/p^n Z, hypergeometric polynomials and binomial congruences
Kartik Prasanna
University of Michigan
https://sites.lsa.umich.edu/kartikp/
Date(s) : 01/07/2025 iCal
14h00 - 15h00
Let R = Z/p^n Z. The representation theory of GL_2 (R) over R-modules is well studied for n=1 but there is not much known for n>1. In this talk, I will describe a single result in the R=Z/p^n Z case, that hints at a larger story. The proof of this result is elementary and eventually reduces to verifying some explicit (but difficult to prove) binomial congruences. It suggests some interesting connections between the archimedean representation theory of Sp(4), hypergeometric polynomials and representations of GL_2 over p-adic rings. I will also explain the motivation for considering this problem, which came from our attempt to solve a certain p-adic differential equation on a Siegel modular variety. This is joint work with Atsushi Ichino.
Emplacement
I2M Luminy - TPR2, Salle de Séminaire 304-306 (3ème étage)
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