Eigenvalue problem and a new product in the cohomology of flag varieties

(Joint work with Shrawan Kumar) Motivated by Horn's conjecture and Eigenvalue problems (eg. possible eigenvalues of products of unitary matrices and saturation conjectures, which I will review), we define a new (commutative and associative) product on the cohomology of the homogenous spaces G/P. This product is a certain deformation of the classical product.

This new product is then used to give a more efficient solution of the eigenvalue problem and the problem of determining the existence of G-invariants in the tensor product of irreducible representations of G (this comes from a study of optimally destabilising one parameter subgroups in Geometric Invariant Theory).

If time permits, I will also talk about the relation of this new product to the problem of non-vanishing Schubert structure constants (in a G/P).

Refreshments will be served at 2:45 p.m. (MATX 1115, Math Faculty Lounge).