Super invariant theory in positive characteristic

TL;DR

This paper investigates the invariant theory of the general linear supergroup over fields of positive characteristic, revealing conditions for faithful symmetric group actions and limitations in generating all invariants.

Contribution

It provides new insights into the action of symmetric groups on tensor superspaces and clarifies when they generate all invariants in positive characteristic.

Findings

Symmetric group algebra acts faithfully under certain conditions.

Symmetric group does not always generate all invariants.

Results depend on the characteristic of the field.

Abstract

We study invariant theory of the general linear supergroup in positive characteristic. In particular, we determine when the symmetric group algebra acts faithfully on tensor superspace and demonstrate that the symmetric group does not always generate all invariants.