Astrid an Huef
(University of New South Wales)
Friday 27th May, 12.0512.55pm, 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
finitedimensional 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.
