Stabilization of Kac polynomials along root strings

2025/05/08 by Vladyslav Zveryk, Zveryk, Vladyslav · 1 citation
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #Mathematical Dynamics and Fractals #Meromorphic and Entire Functions #Polynomial and algebraic computation #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2505.05439

openalex publication_date 2025/05/08 · openalex created_date 2025/10/18 · openalex updated_date 2026/07/30

Abstract

We study the stabilization behavior of cohomology groups associated with moduli spaces of quiver representations for a fixed quiver Q. Under mild conditions on a dimension vector δ, we show that the dimensions of these cohomology groups stabilize when a sufficiently large multiple of δ is added. We derive explicit formulas for the stabilized dimensions and, in particular, obtain stabilization of the coefficients of Kac polynomials.

Citations

• Quiver varieties and root multiplicities in rank 3
• Positivity of Kac polynomials and DT-invariants for quivers
• Kac's conjecture from Nakajima quiver varieties
• Moduli of representations of quivers
• Quiver varieties and Hilbert schemes
• Absolutely indecomposable representations and Kac-Moody Lie algebras (with an appendix by Hiraku Nakajima)
• Geometry of the Moment Map for Representations of Quivers

Cited by

• Harder-Narasimhan Filtration on Moment Map for Quiver Representations

Related

• Positivity of Kac polynomials and DT-invariants for quivers
• Kac polynomials and Lie algebras associated to quivers and curves
• A refinement of the Kac polynomials for quivers with enough loops
• Positivity for toric Kac polynomials in higher depth
• The moduli space of generalized quivers