Representations of Double Affine Lie algebras

Details Representations of Double Affine Lie algebras Representations of Double Affine Lie algebras

2002-05-29

arxiv.org/abs/math/0205312v1

Mathematics

Quantum Algebra

Scientific paper

We study representations of the double affine Lie algebra associated to a simple Lie algebra. We construct a family of indecomposable integrable representations and identify their irreducible quotients. We also give a condition for the indecomposable modules to be irreducible, this is analogous to a result in the representation theory of quantum affine algebras. Finally, in the last section of the paper, we show, by using the notion of fusion product, that our modules are generically reducible.

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