Representations of loop groups as factorization module categories

TL;DR

This paper demonstrates a full embedding of the 2-category of categorical loop group representations into the 2-category of factorization module categories related to the affine Grassmannian, revealing deep structural connections.

Contribution

It establishes a fully faithful embedding of categorical loop group representations into factorization module categories, linking representation theory and geometric structures.

Findings

Categorical representations of loop groups embed into factorization module categories.

The embedding is fully faithful, preserving morphisms and structures.

Connects algebraic and geometric perspectives in representation theory.

Abstract

We show that the (2-)category of categorical representations of the loop group embeds fully faithfully into the (2-)category of factorization module categories with respect to the affine Grassmannian.