# Journal of the Ramanujan Mathematical Society

Volume 34, Issue 1, March 2019 pp. 1–20.

Integrable irreducible representations of Toroidal Lie
algebras

**Authors**:
Tanusree Khandai

**Author institution:**Institute of Mathematics and Applications, Bhubaneswar, Odisha 751 003, India

**Summary: **
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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