Representations of twisted loop algebras and their block decompositions

11/27/2007 - 12:15pm
Prasad Senesi (University of California, Riverside)

We investigate the category of finite-dimensional representations of a twisted affine Kac-Moody algebra. This category is not semisimple, so it is natural to search for its block decomposition. We will begin by describing the block decomposition of an Abelian category and giving some examples of categories of representations which are not semisimple. We will then provide a parametrization of the blocks of the category of finte-dimensional modules for an algebra of type $ A_3^{(2)} $, and describe how this decomposition is related to the decomposition corresponding to the untwisted algebra of type $ A_3^{(1)} $.

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