Quantum groups and quantum cohomology

Vassily Gorbounov (University of Aberdeen)

Tuesday 6th November, 2012 15:00-16:00 Maths 325


We discuss the far reaching extension of the correspondence between the cohomology of the tangent spaces of the partial flag manifolds and the weight subspaces of the tensor product of the fundamental representation of gl(n). 

Under this correspondence the quantum D-module of the tangent to a partial flag manifold corresponds to the dynamical differential equation associated with the Knizhnik-Zamolodchikov equation restricted to the appropriate weight space. Such a correspondence in the case of full flags was conjectured by Okounkov and proved recently. The key tool in the proof is the action of the Yangian on both sides of this correspondence.

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