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arXiv · 2202.02855

On the Connes-Kasparov isomorphism, I: The reduced C*-algebra of a real reductive group and the K-theory of the tempered dual

Pierre Clare·Nigel Higson·Yanli Song·Xiang Tang
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Abstract

This is the first of two papers dedicated to the computation of the reduced C*-algebra of a connected, linear, real reductive group up to Morita equivalence, and the verification of the Connes-Kasparov conjecture for these groups. These results were originally announced by Antony Wassermann in 1987. In Part I we shall give details of the C*-algebraic Morita equivalence, and then compute the Connes-Kasparov morphism subject to some results in tempered representation theory that we shall prove in Part II using tools from David Vogan's classification of the tempered dual.

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Pierre Clare, Nigel Higson, Yanli Song, Xiang Tang. 2022-02-06. On the Connes-Kasparov isomorphism, I: The reduced C*-algebra of a real reductive group and the K-theory of the tempered dual. https://arxiv.org/abs/2202.02855

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