Compositio Mathematica

Representations of Extended Affine Lie Algebras Coordinatized by Certain Quantum Tori

Yun Gao a1
a1 Department of Mathematics and Statistics, York University, Toronto, Ontario, Canada M3J 1P3. E-mail:

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An irreducible representation of the extended affine Lie algebra of type $A_{n-1}$ coordinatized by a quantum torus of ν variables is constructed by using the Fock space for the principal vertex operator realization of the affine Lie algebra ${\widetilde{gl}_{n}$.

Key Words: affine Lie algebra; vertex operator; quantum torus.