Inventiones mathematicae

, Volume 155, Issue 3, pp 537–559

Absolutely indecomposable representations and Kac-Moody Lie algebras


DOI: 10.1007/s00222-003-0329-0

Cite this article as:
Crawley-Boevey, W. & Van den Bergh, M. Invent. math. (2004) 155: 537. doi:10.1007/s00222-003-0329-0


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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© Springer-Verlag 2003

Authors and Affiliations

  1. 1.Department of Pure MathematicsUniversity of LeedsLeedsUK
  2. 2.Departement WNILimburgs Universitair CentrumDiepenbeekBelgium