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Theta correspondence via C*-algebras of groups

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If you have a question about this talk, please contact Rong Zhou.

Theta correspondence is a major theme in the theory of automorphic forms and in representation theory. In a nutshell, the correspondence sets up a bijection between certain sets of smooth admissible irreps of a pair of reductive groups G,H which sit as each others’ centralizers in a larger symplectic group.

In joint work with Bram Mesland (Leiden), we showed that the theta correspondence, in many cases, can be interpreted within the framework of Rieffel’s induction theory for representations of C*-algebras. This interpretation reveals some new fundamental features: the theta correspondence is functorial and is continuous with respect to weak containment. In the talk, I will explain our approach and time permitting, will discuss some further applications. Many of the results I will discuss can be found in the preprint arXiv:2207.13484.

This talk is part of the Number Theory Seminar series.

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