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arXiv · 2109.08905

Counting Semistable Representations of Quivers over Finite Fields

Jiuzhao Hua
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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.

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Jiuzhao Hua. 2021-09-18. Counting Semistable Representations of Quivers over Finite Fields. https://arxiv.org/abs/2109.08905

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