Non symmetric quantum loop groups and K-theory

TL;DR

This paper develops a geometric framework for quantum loop groups, including non-symmetric types, using critical K-theory, extending Nakajima's symmetric case and constructing new simple modules.

Contribution

It generalizes the Nakajima construction to non-symmetric types and provides a new geometric method for constructing simple modules.

Findings

Realized quantum loop groups of arbitrary types via critical K-theory.

Extended Nakajima's symmetric construction to non-symmetric types.

Provided a new geometric construction of simple modules.

Abstract

We realize the quantum loop groups and shifted quantum loop groups of arbitrary types, possibly non symmetric, using critical K-theory. This generalizes the Nakajima construction of symmetric quantum loop groups via quiver varieties to non symmetric types. We also give a new geometric construction of some simple modules of both quantum loop groups and shifted quantum loop groups.