On the Connes–Kasparov isomorphism, II: The Vogan classification of essential components in the tempered dual

Pierre Clare, Nigel Higson, Yanli Song

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Abstract

This is the second of two papers dedicated to the computation of the reduced C*-algebra of a connected, linear, real reductive group up to C*-algebraic Morita equivalence, and the verification of the Connes–Kasparov conjecture in operator K-theory for these groups. In Part I we presented the Morita equivalence and the Connes–Kasparov morphism. In this part we shall compute the morphism using David Vogan’s description of the tempered dual. In fact we shall go further by giving a complete representation-theoretic description and parametrization, in Vogan’s terms, of the essential components of the tempered dual, which carry the K-theory of the tempered dual.

Original languageEnglish (US)
Pages (from-to)111-141
Number of pages31
JournalJapanese Journal of Mathematics
Volume19
Issue number1
DOIs
StatePublished - Apr 2024

All Science Journal Classification (ASJC) codes

  • General Mathematics

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