Operator K-Theory and Tempiric Representations

Jacob Bradd; Nigel Higson; Robert Yuncken

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arXiv · 2412.18924

Operator K-Theory and Tempiric Representations

Jacob Bradd·Nigel Higson·Robert Yuncken

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Abstract

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.

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BibTeX RIS

Jacob Bradd, Nigel Higson, Robert Yuncken. 2024-12-25. Operator K-Theory and Tempiric Representations. https://arxiv.org/abs/2412.18924

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