A New Class of Representations of EALA Coordinated by Quantum Tori in Two Variables

Abstract

AbstractWe study the representations of extended affine Lie algebraswhereqisN-th primitive root of unity (ℂqis the quantum torus in two variables). We first prove that⊕for a suitable number of copies is a quotient of. Thus any finite dimensional irreducible module for⊕lifts to a representation of. Conversely, we prove that any finite dimensional irreducible module forcomes from above. We then construct modules for the extended affine Lie algebraswhich is integrable and has finite dimensional weight spaces.