Symmetric pairs and branching laws

Overview & Synopsis

Let G be a compact connected Lie group and let H be a subgroup fixed by an involution. A classical result assures that the action of the complex reductive group H_C on the flag variety F of G admits a finite number of orbits. In this article we propose a formula for the branching coefficients of the symmetric pair (G,H) that is parametrized by H_C\F .