Branching laws for square integrable representations

VARGAS, JORGE A.

Symposium on Representation Theory 2008

Año: 2008 vol. 1 p. 10 - 21

We fix  $H    subset G $ reductive, connected matrix groups and $pi$ an irreducible square integrable representation of $G.$ Whenever $G$ is compact (resp. $H $ is a maximal compact subgroup) the multiplicity of each irreducible $H-$factor of $pi$ restricted to $H $ may be computed in terms of: infinitesimal characters (resp. Harish Chandra parameters), Weyl group, and ONE partition function, Kostant-Heckman (resp. Blattner) formulae. Assume  $pi, H $ are so that $pi$ restricted to $H$ is admissible, in joint work with Michel Duflo, we have obtained a sufficient condition to express  the multiplicity of each irreducible factor in the framework of above. We also show   the formula holds for $(G,H)$ a symmetric pair and provide examples.