Note on Trace Class Groups

2019/04/26 by Gerrit van Dijk, van Dijk, Gerrit
Social Sciences · #22D10 #43A80 #46C05 #FOS: Mathematics #Functional Analysis (math.FA) #Migration, Ethnicity, and Economy #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1904.11789

openalex publication_date 2019/04/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A Lie group G is called a trace class group if for every irreducible unitary representation R of G and every C-infinity function f with compact support the operator R(f) is of trace class. In this note we prove that the semidirect product of Rⁿ and a real semisimple algebraic subgroup G of GL(n;R) is a trace class group only if G is compact. The converse has been shown elsewhere. We also make a descent start with the study of semidirect products with Heisenberg-type groups.

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