Intertwining operators and geometry

Theta correspondence via C*-algebras

22 janv. 2025, 11:30

50m

Amphithéâtre Hermite (Institut Henri Poincaré)

Orateur

Bram Mesland (Universiteit Leiden)

Description

In this talk I will discuss how the well-known explicit construction of the local theta correspondence by J.S. Li has a simple interpretation in terms of induced representations group $C^{\ast }$-algebras in the sense of M.A.Rieffel. This picture allows us deduce that in the standard cases where Li’s method works, local theta correspondence arises from a continuous functor. In special cases, the functor implements a continuous equivalence of representation categories called strong Morita equivalence. No background in $C^{\ast }$-algebras is required for this talk, as I will introduce the necessary concepts along the way. This is joint work with Magnus Goffeng (Lund) and Haluk Sengun (Sheffield).