The braided monoidal structure of tube algebra representations

TL;DR

This paper constructs a braided monoidal structure with twist on the representations of the tube algebra of a spherical semisimple multitensor category and shows its equivalence with the Drinfeld center of the ind-category.

Contribution

It introduces a new braided monoidal structure on tube algebra representations and establishes an equivalence with the Drinfeld center, extending known linear equivalences.

Findings

Established a braided monoidal structure with twist for tube algebra representations.

Proved the category is braided tensor equivalent to the Drinfeld center of the ind-category.

Extended the linear equivalence to a braided tensor equivalence.

Abstract

We consider the tube algebra of a spherical semisimple multitensor category $\mathcal{X}$, and construct a braided monoidal structure with twist for its representations. We further show that this category is braided tensor equivalent with the Drinfeld center of the ind-category of $\mathcal{X}$, extending the well-known linear equivalence.