Orthogonal matrix invariants

TL;DR

This paper studies the algebra of invariants under the action of the orthogonal group on multiple matrices, describing relations between generators and the maximal degree of minimal generating sets over fields with characteristic not two.

Contribution

It provides a detailed description of relations among generators and bounds on the degrees of minimal generators for the invariant algebra under orthogonal group actions.

Findings

Relations between generators are explicitly described.

Maximal degree of minimal generators is characterized with deviation 3.

Results apply to fields with characteristic not two.

Abstract

The orthogonal group acts on the space of several $n\times n$ matrices by simultaneous conjugation. For an infinite field of characteristic different from two, relations between generators for the algebra of invariants are described. As an application, the maximal degree of elements of a minimal system of generators is described with deviation $3$. This note contains concise but precise description of the results. All proofs can be found in arXiv: 0902.4266 and arXiv: 1011.5201.