Journal of Lie Theory 33 (2023), No. 3, 747--762
Copyright Heldermann Verlag 2023
Classification of Irreducible Integrable Modules for Extended Affine Lie Algebras with Center Acting Trivially
Santanu Tantubay
Dept. of Mathematics, Harish-Chandra Research Institute, Jhunsi, Prayagraj, India
santanutantubay@hri.res.in
Punita Batra
Dept. of Mathematics, Harish-Chandra Research Institute, Jhunsi, Prayagraj, India
batra@hri.res.in
We classify the irreducible integrable modules for the twisted toroidal extended affine Lie algebras with finite dimensional weight spaces where the finite dimensional center acts trivially. S. E. Rao, S. S. Sharma and P. Batra [Integrable modules for twisted toroidal extended affine Lie algebras, J. Algebra 556 (2020) 1057--1072] have classified such modules for twisted toroidal extended affine Lie algebras (with n ≥ 3), where the finite dimensional center acts nontrivially. C. Fulin, L. Zhiqiang and S. Tan [Classification of integrable representations for toroidal extended affine Lie algebras, J. Algebra 514 (2021) 1--37], classified such modules for non twisted toroidal extended affine algebras only for two variables. Our results are valid for any n in case of twisted toroidal extended affine Lie algebras with the finite dimensional center acting trivially. We prove that the universal central extension part acts trivially on the modules and our modules turn out to be the highest weight modules.
Keywords: Twisted toroidal extended affine Lie algebras, integrable modules.
MSC: 17B67, 17B66.
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