Asymptotic behaviour of Kac polynomials
Representation Theory
2025-02-10 v4 Algebraic Geometry
Abstract
We conjecture a formula supported by computations for the valuation of Kac polynomials of a quiver, which only depends on the number of loops at each vertex. We prove a convergence property of renormalized Kac polynomials of quivers when increasing the number of arrows: they converge in the ring of power series, with a linear rate of convergence. Then, we propose a conjecture concerning the global behaviour of the coefficients of Kac polynomials. All computations were made using SageMath.
Cite
@article{arxiv.2003.06929,
title = {Asymptotic behaviour of Kac polynomials},
author = {Lucien Hennecart},
journal= {arXiv preprint arXiv:2003.06929},
year = {2025}
}
Comments
Augmented version. 20 pages. 7 figures. Part of the conjecture of the previous version is now proved. Correction of some inacurracies