Work

Operator K-Theory and Tempiric Representations

Year: 2024

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2412.18924

Authors: Bradd, Jacob, Higson, Nigel, Yuncken, Robert

Institutions: Institut Élie Cartan de Lorraine, Université de Lorraine, Pennsylvania State University

Language: English

Topic: Advanced Algebra and Geometry

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Stanley Medical Research Institute, Agence Nationale de la Recherche, University of New South Wales, University of Wollongong

Awards: FRG: Collaborative Research: The Hypoelliptic Laplacian, Noncommutative Geometry, and Applications to Representations and Singular Spaces, Operator algebras and representation theory of Lie groups and groupoids

OpenAlex ID: W4405901424

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