The Mackey bijection for complex reductive groups and continuous fields of reduced group C*-algebras

Nigel Higson; Angel Roman

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arXiv · 1908.11008

The Mackey bijection for complex reductive groups and continuous fields of reduced group C*-algebras

Nigel Higson·Angel Roman

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Abstract

The purpose of this paper is to make a further contribution to the Mackey bijection for a complex reductive group G, between the tempered dual of G and the unitary dual of the associated Cartan motion group. We shall construct an embedding of the C*-algebra of the motion group into the reduced C*-algebra of G, and use it to characterize the continuous field of reduced group C*-algebras that is associated to the Mackey bijection. We shall also obtain a new characterization of the Mackey bijection using the same embedding.

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Nigel Higson, Angel Roman. 2019-08-29. The Mackey bijection for complex reductive groups and continuous fields of reduced group C*-algebras. https://arxiv.org/abs/1908.11008

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