2024/12/10 by Magnus Goffeng, Goffeng, Magnus, Bram Mesland +3
Mathematics · #11F27 #22D25 #22E50 #22E55 #46L08 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Holomorphic and Operator Theory #Number Theory (math.NT) #Operator Algebras (math.OA) #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2412.07501
openalex publication_date 2024/12/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.