Asymptotic behaviour of Kac polynomials
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2020
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| _version_ | 1866913681886937088 |
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| author | Hennecart, Lucien |
| author_facet | Hennecart, Lucien |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2003_06929 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Asymptotic behaviour of Kac polynomials Hennecart, Lucien Representation Theory Algebraic Geometry 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. |
| title | Asymptotic behaviour of Kac polynomials |
| topic | Representation Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2003.06929 |