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arXiv · 0811.1569

Kac's conjecture from Nakajima quiver varieties

Tamas Hausel
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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.

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Tamas Hausel. 2010-03-15. Kac's conjecture from Nakajima quiver varieties. https://arxiv.org/abs/0811.1569

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