Lie Groups and Representation Theory

Seminar information archive ~05/22Next seminarFuture seminars 05/23~

Date, time & place Tuesday 16:30 - 18:00 126Room #126 (Graduate School of Math. Sci. Bldg.)


16:30-18:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Jorge Vargas (FAMAF-CIEM, C\'ordoba)
Liouville measures and multiplicity formulae for admissible restriction of Discrete Series
[ Abstract ]
Let $H \\subset G$ be reductive matrix Lie groups. We fix a square integrable irreducible representation $\\pi$ of $G.$
Let $\\Omega $ denote the coadjoint orbit of the Harish-Chandra parameter of $\\pi.$

Assume $\\pi$ restricted to $H$ is admissible. In joint work with Michel Duflo, by means of "discrete" and "continuos" Heaviside functions we relate the multiplicity of each irreducible $H-$factor of $\\pi$ restricted to $H$ and push forward to $\\mathfrak h^\\star$ of the Liouville measure for $\\Omega.$ This generalizes work of Duflo-Heckman-Vergne.
[ Reference URL ]