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Integrable Irreducible Representations of Toroidal Lie Algebras


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1 Institute of Mathematics and Applications, Bhubaneswar, Odisha 751 003, Iceland
     

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A classification of the irreducible integrable representations with finite-dimensional weight spaces of toroidal Lie algebras was obtained in [R3]. In [CFK], adopting an approach via Weyl modules it was shown that in the case when the central elements act trivially, the results of [R3] hold for any Lie algebra of the form g ⊗ A, where g is a finite-dimensional Lie algebra and A is a finitely generated commutative algebra with unity. In this paper, adopting the approach of [CFK,L] we give a reproof the results of [R3]. In addition we establish a necessary and sufficient condition under which two such irreducible modules are isomorphic.
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  • Integrable Irreducible Representations of Toroidal Lie Algebras

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Authors

Tanusree Khandai
Institute of Mathematics and Applications, Bhubaneswar, Odisha 751 003, Iceland

Abstract


A classification of the irreducible integrable representations with finite-dimensional weight spaces of toroidal Lie algebras was obtained in [R3]. In [CFK], adopting an approach via Weyl modules it was shown that in the case when the central elements act trivially, the results of [R3] hold for any Lie algebra of the form g ⊗ A, where g is a finite-dimensional Lie algebra and A is a finitely generated commutative algebra with unity. In this paper, adopting the approach of [CFK,L] we give a reproof the results of [R3]. In addition we establish a necessary and sufficient condition under which two such irreducible modules are isomorphic.

References