Abstract:
We study semisimple subgroups of semisimple complex Lie groups, say G'<G, from various points of view: structural (the theory of roots and weights); geometric (G'-actions on the flag variety G/B); representation/invariant theoretic (branching laws for decomposition of irreducible G-modules over G'). The Borel-Weil theorem and the Geometric Invariant Theory of Hilbert-Mumford provide a relation between the geometric and the representation theoretic viewpoints. We shall explore this relation and deduce some results about the structure of the (generalized) Littlewood-Richardson cone. We also show that, under certain conditions, a single well-chosen GIT-quotient of G/B by G' encodes the complete information on G'-invariants in irreducible G-modules.
The talk will be based on a joint work with Henrik Seppänen.