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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Dedicated to Idun Reiten on the occasion of her sixtieth birthday
Mathematics Subject Classification (1991)
16G20, 17B67
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Crawley-Boevey, W., Van den Bergh, M. Absolutely indecomposable representations and Kac-Moody Lie algebras. Invent. math. 155, 537–559 (2004). https://doi.org/10.1007/s00222-003-0329-0
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DOI: https://doi.org/10.1007/s00222-003-0329-0