Department of Mathematics,
University of California San Diego
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Colloquium / Math 209: Number Theory Seminar
Marie-France Vigneras
Jussieu
Asymptotics of $p$-adic groups, mostly $SL_2$
Abstract:
Let $p$ be a prime number and $ Q_p$ the field of $p$-adic numbers.
The representations of a cousin of the Galois group of an algebraic closure of $ Q_p$ are related (the {\bf Langlands's bridge}) to the representations of reductive $p$-adic groups, for instance $SL_2(Q_p), GL_n(Q_p) $. The irreducible representations $\pi$ of reductive $p$-adic groups are easier to study than those of the Galois groups but they are rarely finite dimensional. Their classification is very involved but their behaviour around the identity, that we call the ``asymptotics'' of $\pi$, are expected to be more uniform. We shall survey what is known (joint work with Guy Henniart), and what it suggests.
March 13, 2025
2:00 PM
APM 6402
Research Areas
Number Theory****************************
