Integrable representations for toroidal extended affine Lie algebras

Let g be any untwisted affine Kac-Moody algebra, mu any fixed complex number, and (g) over tilde(mu) the corresponding toroidal extended affine Lie algebra of nullity two. For any k-tuple lambda = (lambda(1), . . . , lambda(k)) of weights of g, and k-tuple a = (a(1), . . . , a(k)) of distinct non-zero complex numbers, we construct a class of modules (V) over tilde(lambda, a) for the extended affine Lie algebra (g) over tilde(mu). We prove that the ( g) over tilde(mu)-module (V) over tilde(lambda, a) is completely reducible. We also prove that the (g) over tilde(mu)-module (V) over tilde(lambda, a) is integrable when all weights lambda(i) in lambda are dominant. Thus, we obtain a new class of irreducible integrable weight modules for the toroidal extended affine Lie algebra (g) over tilde(mu). (C) 2018 Published by Elsevier Inc.