Mathematische Gesellschaft am 23.01.2014

Donnerstag, 23.1.2014, 16.45 Uhr, Sitzungszimmer


Valdemar Tranov, Bochum

"Branching laws and the Borel-Weil-Bott theorem"


Abstract:

Let G' < G be an embedding of complex semisimple Lie groups. One of the fundamental problems in representation theory is to understand the decomposition of a given irreducible G-module V into irreducible G'-components. Another important problem is to understand the G'-orbits in the flag variety G/B. These two problems are related and we shall discuss some of the relations. Specifically, we shall define a type of components in V related to closed G'-orbits in G/B via the Borel-Weil-Bott theorem. This theorem states that every irreducible G-module may be obtained as the cohomology of a line bundle on G/B. Thus we shall study restrictions of line bundles along embeddings of flag varieties, and conditions for nonvanishing of the pullbacks in cohomology. The main tool are Kostant's harmonic representatives in Lie algebra cohomology.