Colloquium
3:00 p.m., Friday (October 21, 2005)
MATH ANNEX 1100
Prakash Belkale
UNC at Chapel Hill
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 Ginvariants 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 nonvanishing Schubert structure constants (in a G/P).
Refreshments will be served at 2:45 p.m. (MATX 1115, Math Faculty Lounge).
