MODULES FOR THE CORE OF EXTENDED AFFINE LIE ALGEBRAS OF TYPE A(1) WITH COORDINATES IN RANK 2 QUANTUM TORI

摘要

We construct a Lie algebra L from rank 3 quantum tori and show that it is isomorphic to the core of extended affine Lie algebras of type A(1). Then we construct two classes-which turn out to be exhaustive- of irreducible Z-graded highest weight L-modules and give necessary and sufficient conditions for these modules to have finite-dimensional homogeneous subspaces. As a consequence, we also determine all the irreducible Z-graded L-modules with nonzero center and finite-dimensional homogeneous subspaces.