Smallness problem for quantum affine algebras and quiver varieties
Abstract
The geometric small property (Borho-MacPherson) of projective morphisms implies a description of their singularities in terms of intersection homology. In this paper we solve the smallness problem raised by Nakajima (math.QA/0105173) for certain resolutions of quiver varieties (analogs of the Springer resolution) : for Kirillov-Reshetikhin modules of simply-laced quantum affine algebras, we characterize explicitly the Drinfeld polynomials corresponding to the small resolutions. We use an elimination theorem for monomials of Frenkel-Reshetikhin q-characters that we establish for non necessarily simply-laced quantum affine algebras. We also refine results of (math.QA/0501202) and extend the main result to general simply-laced quantum affinizations, in particular to quantum toroidal algebras (double affine quantum algebras).
Cite
@article{arxiv.math/0607526,
title = {Smallness problem for quantum affine algebras and quiver varieties},
author = {David Hernandez},
journal= {arXiv preprint arXiv:math/0607526},
year = {2008}
}
Comments
33 pages; accepted for publication in Annales Scientifiques de l'Ecole Normale Superieure