Pieri type rules and $GL(2|2)$ tensor products

TL;DR

This paper derives a closed formula for tensor products of mixed tensors in Deligne's category and applies it to compute tensor products of maximal atypical irreducible representations of GL(2|2).

Contribution

It introduces a new closed-form formula for mixed tensor products in Deligne's category and applies it to specific supergroup representations.

Findings

Closed formula for mixed tensor products in Deligne's category

Explicit tensor product computations for GL(2|2) representations

Enhanced understanding of supergroup representation tensor products

Abstract

We derive a closed formula for the tensor product of a family of mixed tensors using Deligne's interpolating category $Rep(GL_{0})$. We use this formula to compute the tensor product between any two maximal atypical irreducible $GL(2|2)$-representations.