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Qu茅bec-Vermont Number Theory Seminar

Title:听Invariant听norms听on the p-adic Schrodinger representation.

础产蝉迟谤补肠迟:听Motivated by questions about a p-adic Fourier transform, we study听invariant听norms听on the p-adic Schr枚dinger representations of Heisenberg groups. These Heisenberg groups are p-adic, and the Schrodinger representations are explicit irreducible smooth representations that play听an important role in their representation theory.听
Classically, the field of coefficients is taken to be the complex numbers and, among other things, one studies the unitary completions of the representations (which are well understood). By taking the field of coefficients to be an extension of the p-adic numbers, we can consider completions that better capture the p-adic topology, but at the cost of losing the Haar measure and the $L^2$-norm. Nevertheless, we establish a rigidity property for a family of听norms听(parametrized by a Grassmannian) that are听invariant听under the action of the Heisenberg group.
The irreducibility of some Banach representations follows as a result. The proof uses "q-arithmetics".

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For Zoom details, please contact: martinez [at] crm.umontreal.ca

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