Kac's conjecture from Nakajima quiver varieties
Hausel T. 2010. Kac’s conjecture from Nakajima quiver varieties. Inventiones Mathematicae. 181(1), 21–37.
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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 certain weight in the corresponding Kac-Moody algebra, which was conjectured by Kac in 1982.
Publishing Year
Date Published
2010-07-01
Journal Title
Inventiones Mathematicae
Acknowledgement
This work has been supported by a Royal Society University Research Fellowship, NSF grants DMS-0305505 and DMS-0604775 and an Alfred Sloan Fellowship 2005-2007.
Volume
181
Issue
1
Page
21 - 37
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Hausel T. Kac’s conjecture from Nakajima quiver varieties. Inventiones Mathematicae. 2010;181(1):21-37. doi:10.1007/s00222-010-0241-3
Hausel, T. (2010). Kac’s conjecture from Nakajima quiver varieties. Inventiones Mathematicae. Springer. https://doi.org/10.1007/s00222-010-0241-3
Hausel, Tamás. “Kac’s Conjecture from Nakajima Quiver Varieties.” Inventiones Mathematicae. Springer, 2010. https://doi.org/10.1007/s00222-010-0241-3.
T. Hausel, “Kac’s conjecture from Nakajima quiver varieties,” Inventiones Mathematicae, vol. 181, no. 1. Springer, pp. 21–37, 2010.
Hausel T. 2010. Kac’s conjecture from Nakajima quiver varieties. Inventiones Mathematicae. 181(1), 21–37.
Hausel, Tamás. “Kac’s Conjecture from Nakajima Quiver Varieties.” Inventiones Mathematicae, vol. 181, no. 1, Springer, 2010, pp. 21–37, doi:10.1007/s00222-010-0241-3.
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