The geometric Satake correspondence and the Mirkovic-Vilonen cycles
Joel Kamnitzer (Berkeley and AIM)

The geometric Satake correspondence relates representation theory to the
geometry of the affine Grassmannian. In particular, certain subvarieties
of the affine Grassmanian, called Mirkovic-Vilonen cycles, give bases for
representations of complex semisimple groups. In this talk, we will
explain this result as well as give new results concerning an explicit
description of these cycles. These new results provide a combinatorial
link between MV cycles and Lusztig's canonical basis.

Colloquium, Department of Mathematics, Rice University
October 11, 2007


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