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Finite-dimensional representations of twisted loop algebras

Posted on:2008-09-24Degree:Ph.DType:Dissertation
University:University of California, RiversideCandidate:Senesi, Jagannatha PFull Text:PDF
GTID:1440390005963144Subject:Mathematics
Abstract/Summary:
The notion of a Weyl module, previously defined for the untwisted loop algebras, is extended in part I to the twisted loop algebras. We then describe an identification of the Weyl modules for the twisted loop algebras with suitably chosen Weyl mod ules for the untwisted loop algebras. This identification allows us to use known results in the untwisted case to compute the dimensions and characters of the Weyl modules for the twisted algebras. Part II concerns the block decomposition of the category Cs of finite-dimensional representations of a twisted loop algebra. The parametrization of the blocks of this category for the untwisted affine algebras is used in combination with results from part I to achieve a similar parametrization for the blocks of Cs .
Keywords/Search Tags:Twisted loop algebras, Finite-dimensional representations
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