On Deligne's category $\uRep^{ab}(S_d)$

TL;DR

This paper explores the properties of Deligne's category Rep^{ab}(S_d), establishing a universal property and classifying tensor ideals within the related category Rep(S_d).

Contribution

It introduces a universal property for Deligne's abelian category and classifies tensor ideals in the symmetric group representation category.

Findings

Established a universal property of Rep^{ab}(S_d)

Classified tensor ideals in Rep(S_d)

Provided structural insights into Deligne's categories

Abstract

We prove a universal property of Deligne's category $\uRep^{ab}(S_d)$. Along the way, we classify tensor ideals in the category $\uRep(S_d)$.