Note on Trace Class Groups
Representation Theory
2019-04-29 v1 Functional Analysis
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 R^n 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.
Cite
@article{arxiv.1904.11789,
title = {Note on Trace Class Groups},
author = {Gerrit van Dijk},
journal= {arXiv preprint arXiv:1904.11789},
year = {2019}
}
Comments
7 pages