Journal
INVENTIONES MATHEMATICAE
Volume 181, Issue 1, Pages 21-37Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s00222-010-0241-3
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Funding
- Royal Society University Research
- NSF [DMS-0305505, DMS-0604775]
- Alfred Sloan Fellowship
- EPSRC [EP/G027110/1] Funding Source: UKRI
- Engineering and Physical Sciences Research Council [EP/G027110/1] Funding Source: researchfish
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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 certain weight in the corresponding Kac-Moody algebra, which was conjectured by Kac in 1982.
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