Tensor polynomial identities

TL;DR

This paper characterizes a class of tensor polynomial identities using Young tableaux and introduces a method to evaluate alternating tensor polynomials in tensor product spaces.

Contribution

It provides a complete characterization of specific tensor polynomial identities and a new evaluation method for alternating tensor polynomials.

Findings

Characterization of tensor polynomial identities via Young tableaux

A method to evaluate alternating tensor polynomials in $d^2$ variables

Extension of polynomial identities from matrices to tensor product spaces

Abstract

Tensor polynomial identities generalize the concept of polynomial identities on $d \times d$ matrices to identities on tensor product spaces. Here we completely characterize a certain class of tensor polynomial identities in terms of their associated Young tableaux. Furthermore, we provide a method to evaluate arbitrary alternating tensor polynomials in $d^2$ variables.