q-conjugacy classes in loop groups

TL;DR

This paper classifies twisted conjugacy classes in loop groups of classical types using D_q modules, linking algebraic structures to vector bundles over elliptic curves.

Contribution

It introduces a classification of q-conjugacy classes in classical loop groups via D_q modules, connecting algebraic and geometric perspectives.

Findings

Classification of twisted conjugacy classes achieved

D_q modules linked to vector bundles over elliptic curves

Framework applicable to classical groups

Abstract

We classify twisted conjugacy classes in loop groups, restricted to classical groups. The main tool we used is the so-called D_q module, an object which is related to vector bundles over elliptic curves.