Equidimensional quiver representations and their $U$-invariants

TL;DR

This paper introduces a method for constructing free generators of the field of U-invariants for equidimensional quiver representations, depending on a vertex-arrow assignment, advancing invariant theory in representation spaces.

Contribution

It provides a novel systematic approach to generate U-invariants for equidimensional quivers based on a specific map selection, enhancing understanding of their invariant fields.

Findings

Method for constructing free generators of U-invariants

Dependence of generators on vertex-arrow assignment

Framework applicable to arbitrary equidimensional quivers

Abstract

For an arbitrary equidimensional quiver representation, we proposed the method of construction of a system of free generators of the field of $U$-invariants. The construction of the section and system of generators depends on the choice of a map that assign to each vertex one of the arrows incident to it.