2024/12/25 by Jacob Bradd, Bradd, Jacob, Nigel Higson +3
Mathematics · #Advanced Algebra and Geometry #Spectral Theory in Mathematical Physics #Advanced Operator Algebra Research
paper · pdf · doi:10.48550/arxiv.2412.18924
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.