Finite-dimensional representation theory of loop algebras: a survey

2009/05/30 by Senesi, Prasad
#17B10 #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.0906.0099

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.

Related

• A block decomposition of finite-dimensional representations of twisted loop algebras
• Finite-dimensional irreducible representations of twisted loop algebras of the second kind
• Representations of Affine and Toroidal Lie Algebras
• Representations of Multiloop Algebras
• Finite-dimensional irreducible modules for the three-point \mathfraksl₂ loop algebra