Asymptotic behaviour of Kac polynomials
arXiv:2003.06929 · doi:10.1080/10586458.2021.1926012
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.
Augmented version. 20 pages. 7 figures. Part of the conjecture of the previous version is now proved. Correction of some inacurracies