Vol. 93, No. 1, 1981

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On the irreducibility of an induced representation

John Currie Quigg, Jr.

Vol. 93 (1981), No. 1, 163–179

A unitary representation induced from a normal subgroup of a second countable locally compact group with abelian quotient is irreducible if and only if (i) the inducing representation is irreducible with trivial stability subgroup and (ii) the restriction of the induced representation to the normal subgroup is type I. This is proved in the context of twisted group algebras using a duality result for induced representations which includes the Takesaki duality theorem for crossed products of von Neumann algebras (having separable pre-dual). Examples are given showing that condition (ii) above is not redundant.

Mathematical Subject Classification 2000
Primary: 22D30
Secondary: 22D25, 46L10
Received: 9 April 1980
Revised: 28 July 1980
Published: 1 March 1981
John Currie Quigg, Jr.