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Journal of Lie Theory 23 (2013), No. 2, 383--405
Copyright Heldermann Verlag 2013

Integrable Representations for Extended Affine Lie Algebras Coordinated by Quantum Tori

Fulin Chen
Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, P. R. China

Shaobin Tan
School of Mathematical Sciences, Xiamen University, Xiamen 361005, P. R. China

We realize all irreducible integrable modules for the core of extended affine Lie algebras of type A coordinated by quantum tori with center elements act non-trivially. We also study sufficient and necessary conditions for such modules to be unitary.

Keywords: Extended affine Lie algebra, integrable representation, unitary module, quantum tori.

MSC: 17B10, 17B65, 17B67

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