Group Actions Seminar: Dooley, Ferov

The next Group Actions Seminar will be on Monday 5 September at the University of
Sydney.  The schedule, titles and abstracts are below.  

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12 noon-1pm, Carslaw 350 

Speaker: Anthony Dooley, University of Technology Sydney 

Title: The Kirillov orbit method, wrapping maps and $e$-functions 

Abstract: Kirillov’s character formula gives an expression for the character of an
irreducible representation of a Lie group in terms of the (Euclidean) Fourier transform
of its associated coadjoint orbit.  Wildberger and I re-interpreted this using the
wrapping map, which allows one to transfer Ad-invariant distributions from the Lie
algebra to the Lie group, as a convolution homomorphism.  In this talk, I will describe
how the theory works for compact symmetric pairs (G,K).  The convolution of
$K$-invariant distributions needs to be twisted by the so-called $e$-function, and one
then retrieves the characters of $G/K$ as limits of generalised Bessel functions.  

1-3pm Lunch 

3-4pm, Carslaw 175 

Speaker: Michal Ferov, The University of Newcastle 

Title: Amenable quotients of graph products of groups 

Abstract: A group is amenable if it admits a left-invariant Haar measure (there are many
different equivalent definitions).  It is well known fact that not all groups are
amenable, the easiest example being the free group.  One can then ask: if group G is not
amenable, can we at least homomorphically map every non-trivial element of G onto a
non-trivial element of an amenable group, i.e.  does every non-trivial element of G
survive in some amenable quotient of G? Groups with this property are called residually
amenable.  In the talk I will introduce the graph product of groups, group-theoretic
construction naturally generalising the concept of direct and free product in the
category of groups, and show that the class of residually amenable groups is closed
under forming graph products.  This talk is based on the paper
(http://arxiv.org/abs/1505.05001) co-authored with F.  Berlai.  

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