Classification of irreducible Harish-Chandra modules over the loop-Virasoro algebra

Abstract

The loop-Virasoro algebra is the Lie algebra of the tensor product of the Virasoro algebra and the Laurent polynomial algebra. This paper classifies irreducible Harish-Chandra modules over the loop-Virasoro algebra, which turn out to be highest weight modules, lowest weight modules and evaluation modules of the intermediate series (all wight spaces are 1-dimensional). As a by-product, we obtain a classification of irreducible Harish-Chandra modules over truncated Virasoro algebras. We also determine the necessary and sufficient conditions for highest weigh irreducible modules over the loop-Virasoro algebra to have all finite dimensional weight spaces, as well as the necessary and sufficient conditions for highest weigh Verma modules to be irreducible.

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References in corpus (2)

• Two-toroidal Lie Algebra as Current Algebra of Four-dimensional Kähler WZW Model
• Higher-dimensional WZW Model on Kähler Manifold and Toroidal Lie Algebra

Cited by in corpus (3)

• Irreducible Virasoro modules from tensor products
• Whittaker modules for classical Lie superalgebras
• Classification of Harish-Chandra modules over some Lie algebras related to the Virasoro algebra