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

1998/08/07 by Schiffmann Olivier, Olivier, Schiffmann
Mathematics · #FOS: Mathematics #Quantum Algebra (math.QA) #math.QA

paper · pdf · doi:10.48550/arxiv.math/9808038

Latex, 5 pages, to appear in Comptes Rendus Acad. Sciences

arxiv created 1998/08/07 · arxiv updated 2009/11/30

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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