Abstract: One of the most beautiful and important theorems in representation theory is the Borel-Weil-Bott theorem, which produces all of the irreducible representations of a semi-simple Lie group G (for instance GL_n) in the cohomology groups of a specific algebraic variety X constructed from G.

For the purposes of representation theory these cohomology groups are usually just treated as vector spaces, but because they come from geometry, they have a richer internal structure. In particular, there is a cup product map defined on any two such groups which maps to a third.

It was not previously known how to compute the effects of this map.

This talk will discuss the complete solution to this problem for all semi-simple groups G, as well as the related representation-theoretic problem of which components of a tensor product can be realized through such a cup product map.

Most of the talk will be a discussion of the representation theory of G and the Borel-Weil-Bott theorem.

This is a joint project with Ivan Dimitrov.