University of Sydney Algebra Seminar

Astrid an Huef (University of New South Wales)

Friday 27th May, 12.05-12.55pm, Carslaw 275

Extending representations and the duality of induction and restriction

Let G be a locally compact group and U a unitary representation of a closed subgroup H of G on some Hilbert space. When does U extend to a unitary representation of G on the same space?

For normal subgroups N, Clifford answered this extension problem for finite-dimensional irreducible representations of discrete groups: there is an obstruction to extending the representation in the cohomology group H²(G/N,T), where T is the unit circle. Mackey extended Clifford's results to irreducible representations of locally compact groups: his obstruction lies in a cohomology theory where the cochains are Borel.

I will discuss how a circle of ideas from nonabelian duality for crossed products of C*-algebras is used to study this problem for arbitrary (i.e. not necessarily irreducible) representations.

This is joint work with Steven Kaliszewski, Iain Raeburn and Dana Williams.