Integrable representations for toroidal extended affine Lie algebras.

Abstract Let g be any untwisted affine Kac–Moody algebra, μ any fixed complex number, and g ˜ (μ) the corresponding toroidal extended affine Lie algebra of nullity two. For any k -tuple λ = (λ 1 , ⋯ , λ 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 ˜ (λ , a) for the extended affine Lie algebra g ˜ (μ). We prove that the g ˜ (μ) -module V ˜ (λ , a) is completely reducible. We also prove that the g ˜ (μ) -module V ˜ (λ , a) is integrable when all weights λ i in λ are dominant. Thus, we obtain a new class of irreducible integrable weight modules for the toroidal extended affine Lie algebra g ˜ (μ). [ABSTRACT FROM AUTHOR]