Principal Realization for the extended affine Lie algebra of type $sl_2$ with coordinates in a simple quantum torus with two generators

TL;DR

This paper constructs an explicit irreducible representation of an extended affine $sl_2$ algebra with quantum torus coordinates, using vertex operator formulas akin to those in infinite rank affine algebra theory.

Contribution

It provides a novel explicit construction of irreducible representations for extended affine $sl_2$ algebras with quantum torus coordinates.

Findings

Explicit formulas for irreducible representations using vertex operators

Connection to infinite rank affine algebra $A_{}$ theory

Advancement in understanding quantum torus-based affine algebras

Abstract

We construct an irreducible representation for the extended affine algebra of type $sl_2$ with coordinates in a quantum torus. We explicitly give formulas using vertex operators similar to those found in the theory of the infinite rank affine algebra $A_{\infty}$.