Algebraic Geometry Seminar

Allen KnutsonCornell University
Introduction to Nakajima quiver varieties

Wednesday, September 6, 2017 - 1:20pm
Malott 205

"Geometric representation theory" should perhaps be called instead
"homological"; it is concerned with constructing representations
of important groups and algebras on the homology (of various types)
of certain algebraic varieties, even when the groups don't act
on the varieties themselves. I'll talk about one of the main examples,
the action of a simply-laced Lie group on the top homology of its
associated Nakajima quiver varieties (which I'll define from the ground up).

Subtler, but perhaps more natural, is Nakajima's action of the Yangian
algebra on the total homology. I hope to explain Jimbo's construction
of R-matrices from Yangian modules, and Maulik-Okounkov's combination
of these, interpreting R-matrices geometrically (thereby giving a
natural explanation for my puzzle results from Friday).