Kac's conjecture from Nakajima quiver varieties

• 成果类型: Article
• 署名作者: Hausel, Tamas
• 署名单位: University of Oxford
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-010-0241-3
• 发表日期: 2010
• 页码: 21-37
• 关键词: root systems; REPRESENTATIONS

摘要

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.