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arXiv · 0906.0099

Finite-dimensional representation theory of loop algebras: a survey

Prasad Senesi
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Abstract

We survey some important results concerning the finite--dimensional representations of the loop algebra of a simple complex Lie algebra, and their twisted loop subalgebras. In particular, we review the parametrization and description of the Weyl modules and of the irreducible finite--dimensional representations of such algebras, describe a block decomposition of the (non--semisimple) category of their finite--dimensional representations, and conclude with recent developments in the representation theory of multiloop algebras.

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Prasad Senesi. 2009-08-20. Finite-dimensional representation theory of loop algebras: a survey. https://arxiv.org/abs/0906.0099

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