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

Prasad Senesi

Published 2008-07-25, updated 2009-08-20Version 3

In this paper we consider the category of F^\sigma of finite-dimensional representations of a twisted loop algebra corresponding to a finite-dimensional Lie algebra with non-trivial diagram automorphism. Although F^\sigma is not semisimple, it can be written as a sum of indecomposable subcategories (the blocks of the category). To describe these summands, we introduce the twisted spectral characters for the twisted loop algebra. These are certain equivalence classes of the spectral characters defined by Chari and Moura for an untwisted loop algebra, which were used to provide a description of the blocks of finite--dimensional representations of the untwisted loop algebra. Here we adapt this decomposition to parametrize and describe the blocks of F^\sigma, via the twisted spectral characters.