, Volume 155, Issue 3, pp 537-559
Date: 16 Oct 2003

Absolutely indecomposable representations and Kac-Moody Lie algebras

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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.

Dedicated to Idun Reiten on the occasion of her sixtieth birthday

Mathematics Subject Classification (1991)

16G20, 17B67