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Elliptic quantum groups and their finite-dimensional representations

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I will describe joint work with Sachin Gautam where we give a definition of the category of finite-dimensional representations of an elliptic quantum group which is intrinsic, uniform for all Lie types, and valid for numerical values of the deformation and elliptic parameters. We also classify simple objects in this category in terms of elliptic Drinfeld polynomials. This classification is new even for sl(2), as is our definition outside of type A.