Principal Realization for the extended affine Lie algebra of type $sl_2$   with coordinates in a simple quantum torus with two generators
  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 $A_{\infty}$. 
Stephen Berman and Jacek Szmigielski