Counting Semistable Representations of Quivers over Finite Fields

2021/09/18 by Jiuzhao Hua, Hua, Jiuzhao
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2109.08905

openalex publication_date 2021/09/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we derive a closed formula for the number of isomorphism classes of absolutely indecomposable semistable representations of an arbitrary quiver over a finite field with a fixed dimension vector. This generalises a formula for Kac polynomials given by Hua. A key step in the proof is to show that any representation of a quiver with a nilpotent endomorphism over an arbitrary field admits a structured filtration by subrepresentations compatible with the nilpotent action.

Citations

• Mixed Hodge structures of configuration spaces

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