Operator K-Theory and Tempiric Representations
Representation Theory
2024-12-30 v1 K-Theory and Homology
Operator Algebras
Abstract
David Vogan proved that if is a real reductive group, and if is a maximal compact subgroup of , then every irreducible representation of is included as a minimal -type in precisely one tempered, irreducible unitary representation of with real infinitesimal character, and that moreover it is included there with multiplicity one and is the unique minimal -type in that representation. We shall prove that the Connes-Kasparov isomorphism in operator -theory is equivalent to a -theoretic version of Vogan's result.
Cite
@article{arxiv.2412.18924,
title = {Operator K-Theory and Tempiric Representations},
author = {Jacob Bradd and Nigel Higson and Robert Yuncken},
journal= {arXiv preprint arXiv:2412.18924},
year = {2024}
}