Abstract
These lecture notes are based on Yang’s talk at the MATRIX program Geometric R-Matrices: from Geometry to Probability, at the University of Melbourne, Dec. 18–22, 2017, and Zhao’s talk at Perimeter Institute for Theoretical Physics in January 2018. We give an introductory survey of the results in Yang and Zhao (Quiver varieties and elliptic quantum groups, 2017. arxiv1708.01418). We discuss a sheafified elliptic quantum group associated to any symmetric Kac-Moody Lie algebra. The sheafification is obtained by applying the equivariant elliptic cohomological theory to the moduli space of representations of a preprojective algebra. By construction, the elliptic quantum group naturally acts on the equivariant elliptic cohomology of Nakajima quiver varieties. As an application, we obtain a relation between the sheafified elliptic quantum group and the global affine Grassmannian over an elliptic curve.
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