The Value of the Kac Polynomial at One
Hans Franzen, Thorsten Weist
TL;DR
This paper derives a formula connecting the value of the Kac polynomial at one to the Kac polynomials of a universal covering quiver, using advanced geometric methods involving quiver varieties.
Contribution
It introduces a new formula relating Kac polynomials at one for a quiver and its universal abelian cover, employing torus localization techniques.
Findings
Established a formula for Kac polynomial at one in terms of covering quivers.
Applied torus localization to quiver varieties for the derivation.
Provides new insights into the structure of Kac polynomials.
Abstract
We establish a formula for the value of the Kac polynomial at one in terms of Kac polynomials, evaluated at one, of the universal (abelian) covering quiver by applying torus localization methods to quiver varieties introduced by Hausel--Letellier--Rodriguez-Villegas.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Algebra and Geometry · Algebraic Geometry and Number Theory