Kac's conjecture from Nakajima quiver varieties

Details Kac's conjecture from Nakajima quiver varieties Kac's conjecture from Nakajima quiver varieties

2008-11-10

arxiv.org/abs/0811.1569v2

Mathematics

Representation Theory

12 pages; minor changes, to appear in Inventiones Mathematicae

Scientific paper

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.

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