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

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.

The constant term conjecture is now true for indivisible dimension vectors

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• Counting rational points of quiver moduli
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• Mixed Hodge polynomials of character varieties
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• On Numbers of Tuples of Nilpotent Matrices over Finite Fields under Simultaneous Conjugation
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• All the GIT quotients at once
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