Operator K -theory and tempiric representations

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.