Almost finitary birepresentation theory and applications to affine Soergel bimodules

TL;DR

This paper extends finitary birepresentation theory to infinite Coxeter groups, focusing on classifying simple birepresentations of almost finitary bicategories and analyzing affine type A Soergel bimodules.

Contribution

It generalizes birepresentation theory to infinite groups and provides a classification framework for simple birepresentations in this setting.

Findings

Developed a reduction process for classifying simple birepresentations

Applied theory to affine type A Soergel bimodules

Extended finitary concepts to infinite Coxeter groups

Abstract

In this article, we develop a generalization of finitary birepresentation theory applicable to Soergel bimodules for infinite Coxeter groups. We establish a reduction process for the classification of simple birepresentations of almost finitary bicategories, and consider in detail the case of Soergel bimodules in extended affine type A.