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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/61574A 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 vectorsRings and AlgebrasCombinatorics16G20; 17B67Absolutely indecomposable representations and Kac-Moody Lie algebras (with an appendix by Hiraku Nakajima)text