Operator K-Theory and Tempiric Representations

Fuente: arXiv
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Autori principali: Bradd, Jacob, Higson, Nigel, Yuncken, Robert
Natura: Preprint
Pubblicazione: 2024
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author Bradd, Jacob
Higson, Nigel
Yuncken, Robert
author_facet Bradd, Jacob
Higson, Nigel
Yuncken, Robert
contents David Vogan proved that if $G$ is a real reductive group, and if $K$ is a maximal compact subgroup of $G$, then every irreducible representation of $K$ is included as a minimal $K$-type in precisely one tempered, irreducible unitary representation of $G$ with real infinitesimal character, and that moreover it is included there with multiplicity one and is the unique minimal $K$-type in that representation. We shall prove that the Connes-Kasparov isomorphism in operator $K$-theory is equivalent to a $K$-theoretic version of Vogan's result.
format Preprint
id arxiv_https___arxiv_org_abs_2412_18924
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Operator K-Theory and Tempiric Representations
Bradd, Jacob
Higson, Nigel
Yuncken, Robert
Representation Theory
K-Theory and Homology
Operator Algebras
22E45, 22E46, 46L80
David Vogan proved that if $G$ is a real reductive group, and if $K$ is a maximal compact subgroup of $G$, then every irreducible representation of $K$ is included as a minimal $K$-type in precisely one tempered, irreducible unitary representation of $G$ with real infinitesimal character, and that moreover it is included there with multiplicity one and is the unique minimal $K$-type in that representation. We shall prove that the Connes-Kasparov isomorphism in operator $K$-theory is equivalent to a $K$-theoretic version of Vogan's result.
title Operator K-Theory and Tempiric Representations
topic Representation Theory
K-Theory and Homology
Operator Algebras
22E45, 22E46, 46L80
url https://arxiv.org/abs/2412.18924