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

Anthony Dooley
University of Technology Sydney, Sydney, Australia
5 September, 12 noon, Carslaw 350, University of Sydney

## 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.