The University of Sydney
School of Mathematics and Statistics  
Algebra Seminar  
The University of Sydney USyd Home  MyUni MyUni  Library  Sitemap 
 About the School 
 Research Activities 
 For prospective students 
 For current students 
 School Internal Web Site 

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.