Theta correspondence via group C*-algebras
Operator Algebras
2024-12-11 v1 Number Theory
Representation Theory
Abstract
We prove that the well-known explicit construction of the local theta correspondence by Li has a simple interpretation in terms of group C*-algebras. In particular, we deduce that in two standard cases where Li's method work, local theta correspondence arises from a continuous functor. Moreover, using results from a companion paper, we treat global theta correspondence using C*-algebraic methods. As a byproduct, we exhibit that Rallis inner product formula can be interpreted as a certain natural inclusion being an isometry.
Keywords
Cite
@article{arxiv.2412.07501,
title = {Theta correspondence via group C*-algebras},
author = {Magnus Goffeng and Bram Mesland and Mehmet Haluk Sengun},
journal= {arXiv preprint arXiv:2412.07501},
year = {2024}
}