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Aix-Marseille Université
Institut de Mathématiques de Marseille (I2M) - UMR 7373
Site Saint-Charles : 3 place Victor Hugo, Case 19, 13331 Marseille Cedex 3
Site Luminy : Campus de Luminy - Case 907 - 13288 Marseille Cedex 9

Séminaire

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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