Kac's conjecture from Nakajima quiver varieties
Representation Theory
2010-03-17 v2 Algebraic Geometry
Abstract
We prove a generating function formula for the Betti numbers of Nakajima quiver varieties. We prove that it is a q-deformation of the Weyl-Kac character formula. In particular this implies that the constant term of the polynomial counting the number of absolutely indecomposable representations of a quiver equals the multiplicity of a a certain weight in the corresponding Kac-Moody algebra, which was conjectured by Kac in 1982.
Cite
@article{arxiv.0811.1569,
title = {Kac's conjecture from Nakajima quiver varieties},
author = {Tamas Hausel},
journal= {arXiv preprint arXiv:0811.1569},
year = {2010}
}
Comments
12 pages; minor changes, to appear in Inventiones Mathematicae