Integrable modules for twisted toroidal extended affine Lie algebras

In this paper we classify the irreducible integrable modules for the twisted toroidal extended affine Lie algebras (twisted toroidal EALA, in short) with finite dimensional weight spaces when the finite dimensional center acts non-trivially. Using an automorphism we reduce to the case where K(0 )acts non-trivially and K-i, 1 <= i <= n act trivially. Twisted toroidal EALA has a natural triangular decomposition and we prove that any irreducible integrable module of it with finite dimensional weight spaces is a highest weight module with respect to the above triangular decomposition. The highest weight space is an irreducible module for the zeroth component of the twisted toroidal EALA. We then describe the highest weight space in detail. (C) 2020 Elsevier Inc. All rights reserved.