On Numbers of Semistable Representations of Quivers over Finite Fields

TL;DR

This paper introduces a generating function identity that allows precise calculation of the number of isomorphism classes of absolutely indecomposable semistable quiver representations over finite fields.

Contribution

It provides a new generating function identity to compute the counts of semistable quiver representations over finite fields, advancing understanding in representation theory.

Findings

Derived a generating function identity for counting semistable representations

Enabled exact calculations of isomorphism classes over finite fields

Enhanced methods for studying quiver representations

Abstract

In this paper we prove an identity in terms of generating functions which enables us to calculate the numbers of isomorphism classes of absolutely indecomposable semistable representations of quivers over finite fields.