Tuesday 6 June 2017, 16:00-17:00 in HG03.085
Peter Hochs (University of Adelaide)
K-types of tempered representations
Tempered representations of a semisimple Lie group G are the irreducible unitary representations one needs in the Plancherel decomposition of L^2(G). They are relevant to harmonic analysis because of this, and also occur in the Langlands classification of the larger class of admissible representations. If K< is a maximal compact subgroup, then there is a considerable amount of information in the restriction of a tempered representation to K. In joint work with Yanli Song and Shilin Yu, we give a geometric realisation of these restrictions as indices of Dirac operators on certain homogeneous spaces/coadjoint orbits of G. As an application, we find a geometric expression for the decomposition into irreducibles of the restriction of the representation to K.