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UID:8868@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20250701T140000
DTEND;TZID=Europe/Paris:20250701T150000
DTSTAMP:20251002T091638Z
URL:https://www.i2m.univ-amu.fr/evenements/representations-of-gl_2-over-z-
 pn-z-hypergeometric-polynomials-and-binomial-congruences/
SUMMARY:Kartik Prasanna (University of Michigan): Representations of GL_2 o
 ver Z/p^n Z\, hypergeometric polynomials and binomial congruences
DESCRIPTION:Kartik Prasanna: 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 kno
 wn for n&gt\;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 e
 lementary and eventually reduces to verifying some explicit (but difficul
 t to prove) binomial congruences. It suggests some interesting connection
 s 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 modu
 lar variety. This is joint work with Atsushi Ichino.
CATEGORIES:Séminaire,Représentations des Groupes Réductifs
LOCATION:I2M Luminy - TPR2\, Salle de Séminaire 304-306 (3ème étage)\, 1
 63 Avenue de Luminy\, Marseille\, 13009\, France
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=163 Avenue de Luminy\, Mars
 eille\, 13009\, France;X-APPLE-RADIUS=100;X-TITLE=I2M Luminy - TPR2\, Sall
 e de Séminaire 304-306 (3ème étage):geo:0,0
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