Quantum affine algebras at roots of unity and equivariant K-theory
Abstract
In this short note, we show that the Ginzburg-Vasserot map between the quantum affine algebra of type A(n-1) and the equivariant K-theory group of the Steinberg Variety (of n-step flags in Cd) restricts and remains surjective at the level of the integral forms. In particular, this shows that the parametrization of irreducible, finite-dimensional modules and the Kazhdan-Lusztig multiplicity formulas are valid for the (restricted) specialization at roots of unity.
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