Quantum integrable systems in cohomology theories I
Vassily Gorbounov (University of Aberdeen)  Oberseminar Darstellungstheorie
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When 
Nov 30, 2015 from 04:15 pm to 05:15 pm 
Where  Bonn, Seminarraum MPI, Vivatsgasse 7 
Contact Name  Sachinidis 
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In these lectures we describe a geometric construction of two Yang Baxter algebras, quantum group type objects, each is a degeneration of the socalled six vertex model from statistical physics. These algebras are defined by the Chern classes of the natural vector bundles over partial flag varieties via the convolution construction common in the geometric representation theory. The major ingredient of the construction of a Yang Baxter algebra is the R matrix, which is a part of a solution of the Yang Baxter equation. It turns out that in our case the R matrix encodes the natural relations between the above Chern classes. As an output we obtain a new description of the Schubert calculus on the cohomology of Grassmannians.