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Higher spin representations of the Yangian of sl2 and R-matrices

Algebraic Geometry

Speaker: Yaping Yang, U. of Melbourne
Location: Zoom 939 7121 2537
Start time: Wed, Apr 10 2024, 3:10PM

I will talk about higher spin representations of the Yangian of sl_2.  Consider the algebra homomorphism from the Yangian to the enveloping algebra of sl_2, corresponding to evaluating a function on the complex plane at a point.  The higher spin representations are tensor products of the evaluation pullback of the $\ell_i+1$-dimensional irreducible representations of sl_2, where $\ell_i$ are the highest weights. In my talk, I will give a geometric realization of the higher spin representations in terms of the critical cohomology of representations of the quiver with potential of Bykov and Zinn-Justin. This generalizes the well-known result that the tensor product of fundamental representations of Yangian of sl_2 is isomorphic to the Borel Moore homology of the cotangent bundle of Grassmannians. When time permits, I will also explain the computation of R-matrices.