Absolutely indecomposable representations and Kac-Moody Lie algebras

• 成果类型: Article
• 署名作者: Crawley-Boevey, W; Van den Bergh, M
• 署名单位: University of Leeds; Hasselt University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-003-0329-0
• 发表日期: 2004
• 页码: 537-559
• 关键词: lefschetz trace formula; kleinian singularities; ale spaces; COHOMOLOGY; VARIETIES; QUIVERS; MODULI; CONSTRUCTION; bases

摘要

A conjecture of Kac states that the polynomial counting the number of absolutely indecomposable representations of a quiver over a finite field with given dimension vector has positive coefficients and furthermore that its constant term is equal to the multiplicity of the corresponding root in the associated Kac-Moody Lie algebra. In this paper we prove these conjectures for indivisible dimension vectors.