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University of Sydney Algebra Seminar

Nigel Higson

Friday 6 September, 12-1pm, Place: Carslaw 275

The Mackey bijection

The Mackey bijection identifies irreducible, usually infinite-dimensional, representations of a real reductive group G with the irreducible representations of the Cartan motion group associated to G. Since the latter are quite easy to determine, whereas the former are not, the bijection is a statement of some substance. At the present time, the bijection seems to be best viewed from the perspective of analysis, tempered representations, and even C*-algebras (sorry). But the bijection, though proved, is far from fully understood. I shall try to give an introduction to the topic that is suitable for an algebra seminar.