Absolutely indecomposable representations and Kac-Moody Lie algebras (with an appendix by Hiraku Nakajima)

William Crawley-Boevey; Michel Van den Bergh

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Absolutely indecomposable representations and Kac-Moody Lie algebras (with an appendix by Hiraku Nakajima)

William Crawley-Boevey·Michel Van den Bergh

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Abstract

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.

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William Crawley-Boevey, Michel Van den Bergh. 2001-11-19. Absolutely indecomposable representations and Kac-Moody Lie algebras (with an appendix by Hiraku Nakajima). https://arxiv.org/abs/math/0106009

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