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Quantum affine algebras at roots of unity and equivariant K-theory

Schiffmann Olivier
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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 C^d) 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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Schiffmann Olivier. 1998-08-07. Quantum affine algebras at roots of unity and equivariant K-theory. https://arxiv.org/abs/math/9808038

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