Geometric invariant theory and generalized eigenvalue problem ii

Abstract

Let G be a connected reductive subgroup of a complex connected reductive group ĝ. Fix maximal tori and Borel subgroups of G and ĝ. Consider the cone LR° (G, ĝ) generated by the pairs (v v̂) of strictly dominant characterssuch that V* v; is a submodule of V v;. We obtain a bijective parametrization of the faces of LR°(G, ĝ) as a consequence of general results on GIT-cones. We show how to read the inclusion of faces off this parametrization.