Thick Ideals in Deligne's category $\underline{\operatorname{Re}}\!\operatorname{p}(O_\delta)$

TL;DR

This paper classifies thick ideals in Deligne's category related to orthogonal groups, providing a detailed description of indecomposable objects, tensor product decompositions, and applications to supergroup representations.

Contribution

It offers a complete classification of thick ideals in Deligne's category $0Re ext{p}(O_ ext{delta})$, including indecomposable objects and tensor product structures.

Findings

Classified indecomposable objects in Deligne's category.

Described tensor product decompositions.

Classified indecomposable summands of tensor powers of the standard supergroup representation.

Abstract

We describe indecomposable objects in Deligne's category $\underline{\operatorname{Re}}\!\operatorname{p}(O_\delta)$ and explain how to decompose their tensor products. We then classify thick ideals in $\underline{\operatorname{Re}}\!\operatorname{p}(O_\delta)$. As an application we classify the indecomposable summands of tensor powers of the standard representation of the orthosymplectic supergroup up to isomorphism.