Mirkovic-Vilonen cycles on the affine Grassmannian

  • Date: 01/23/2007
Lecturer(s):

Joel Kamnitzer (American Institute of Mathematics)

Location: 

University of British Columbia

Topic: 

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. Moreover,
their moment map images (the MV polytopes) can be used to understand
the combinatorics of these representations. In this talk, we will
explain these results as well as give new results concerning an
explicit description of these cycles and polytopes. These new results
provide a combinatorial link between MV cycles and Lusztig's canonical
basis.

Other Information: 

UBC Mathematics Department Colloquium Hosted by PIMS-UBC 2007

Sponsor: 

pims