TY - JOUR
T1 - On the Connes–Kasparov isomorphism, II
T2 - The Vogan classification of essential components in the tempered dual
AU - Clare, Pierre
AU - Higson, Nigel
AU - Song, Yanli
N1 - Publisher Copyright:
© The Mathematical Society of Japan and Springer Nature Japan KK, part of Springer Nature 2024.
PY - 2024/4
Y1 - 2024/4
N2 - 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.
AB - 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.
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U2 - 10.1007/s11537-024-2221-1
DO - 10.1007/s11537-024-2221-1
M3 - Article
AN - SCOPUS:85187889350
SN - 0289-2316
VL - 19
SP - 111
EP - 141
JO - Japanese Journal of Mathematics
JF - Japanese Journal of Mathematics
IS - 1
ER -