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## Extending Representations of Subgroups to Groups

### Astrid an Huef

University of New South Wales, Australia

###
Thursday, December 1, 2005

L01 Carson Hall, 4 pm

Tea 3:30 pm, Math Lounge

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

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
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
ways of tackling the extension problem for arbitrary (i.e. not
necessarily irreducible) representations.

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

This talk will be accessible to graduate students.