A note on weight systems which are quantum states

TL;DR

This paper extends a known result that certain $rak{gl}_n$-weight systems are quantum states to include those labeled by symmetric and exterior powers of the defining representation, broadening the class of such systems.

Contribution

It generalizes previous findings by demonstrating that all $rak{gl}_n$-weight systems from symmetric and exterior powers are quantum states.

Findings

All $rak{gl}_n$-weight systems from symmetric powers are quantum states.

All $rak{gl}_n$-weight systems from exterior powers are quantum states.

Extension of previous results to a broader class of weight systems.

Abstract

A result of Corfield, Sati, and Schreiber asserts that $\mathfrak{gl}_n$-weight systems associated to the defining representation are quantum states. In this short note we extend this result to all $\mathfrak{gl}_n$-weight systems corresponding to labeling by symmetric and exterior powers of the defining representation.