Absolutely indecomposable representations and Kac-Moody Lie algebras (with an appendix by Hiraku Nakajima)
Rings and Algebras
2007-05-23 v3 Combinatorics
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.
Keywords
Cite
@article{arxiv.math/0106009,
title = {Absolutely indecomposable representations and Kac-Moody Lie algebras (with an appendix by Hiraku Nakajima)},
author = {William Crawley-Boevey and Michel Van den Bergh},
journal= {arXiv preprint arXiv:math/0106009},
year = {2007}
}
Comments
The constant term conjecture is now true for indivisible dimension vectors