Operator K-Theory and Tempiric Representations
K-théorie analytique et représentations tempiriques
Résumé
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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