Generating invariant rings of quivers in arbitrary characteristic

TL;DR

This paper develops polynomial bounds for matrix semi-invariants and invariants of quivers over fields of any characteristic, using good filtrations and null cone results, advancing understanding of invariant ring generation.

Contribution

It introduces a method to establish polynomial bounds for invariants of quivers in arbitrary characteristic, extending previous results to a broader setting.

Findings

Polynomial bounds for matrix semi-invariants in arbitrary characteristic

Extension of bounds to invariants and semi-invariants of quivers

Application of good filtrations and null cone theory

Abstract

It is well known that the ring of polynomial invariants of a reductive group is finitely generated. However, it is difficult to give strong upper bounds on the degrees of the generators, especially over fields of positive characteristic. In this paper, we make use of the theory of good filtrations along with recent results on the null cone to provide polynomial bounds for matrix semi-invariants in arbitrary characteristic, and consequently for matrix invariants. Our results generalize to invariants and semi-invariants of quivers.