Absolutely indecomposable representations and KacMoody 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 KacMoody Lie algebra. In this paper we prove these conjectures for indivisible dimension vectors.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 June 2001
 arXiv:
 arXiv:math/0106009
 Bibcode:
 2001math......6009C
 Keywords:

 Mathematics  Rings and Algebras;
 Mathematics  Combinatorics;
 16G20;
 17B67
 EPrint:
 The constant term conjecture is now true for indivisible dimension vectors