Eigenvalue Problem and a New Product in Cohomology of Flag Varieties

  • Date: 05/22/2007

Shrawan Kumar (University of North Carolina at Chapel Hill)


University of Washington


This is a report on my joint work with P. Belkale. We define a new
commutative and associative product in the cohomology of any flag
variety G/P (which still satisfies the Poincaré duality) and use this
product to generate certain inequalities which solves the analog of the
classical Hermitian eigenvalue problem for any complex semisimple group
G. Our recipe provides considerable improvement, in general, over the
set of inequalities defined by Berenstein-Sjamaar. In fact, our set of
inequalities form an irredundant system of inequalities. The talk
should be accessible to general mathematical audience.

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10th Anniversary Speaker Series 2007