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Mirkovic-Vilonen cycles and polytopes
Geometry/Topology| Speaker: | Joel Kamnitzer, UC Berkeley |
| Location: | 693 Kerr |
| Start time: | Thu, Apr 14 2005, 3:10PM |
Description
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. More-
over, their moment map images (the MV polytopes) can be used to
understand the combi-
natorics 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.