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arXiv · 2003.06929

Asymptotic behaviour of Kac polynomials

Lucien Hennecart
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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.

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BibTeXRIS

Lucien Hennecart. 2020-03-15. Asymptotic behaviour of Kac polynomials. https://doi.org/10.1080/10586458.2021.1926012

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