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In this paper we consider the category of F^\sigma of finite-dimensionalrepresentations of a twisted loop algebra corresponding to a finite-dimensionalLie algebra with non-trivial diagram automorphism. Although F^\sigma is notsemisimple, it can be written as a sum of indecomposable subcategories (theblocks of the category). To describe these summands, we introduce the twistedspectral characters for the twisted loop algebra. These are certain equivalenceclasses of the spectral characters defined by Chari and Moura for an untwistedloop algebra, which were used to provide a description of the blocks offinite--dimensional representations of the untwisted loop algebra. Here weadapt this decomposition to parametrize and describe the blocks of F^\sigma,via the twisted spectral characters.

A block decomposition of finite-dimensional representations of twisted loop algebras