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- W174945701 abstract "Author(s): Bennett, Matthew Lyle | Advisor(s): Chari, Vyjayanthi | Abstract: The category of graded level zero representations of current Lie algebra shares many properties with other well--known categories which appear in Lie theory and in algebraic groups in characteristic p. In my thesis I explore further similarities. In the first part of my thesis I show that a BGG style reciprocity holds for a category of graded modules for the current algebra. The role of the standard and co--standard modules are played by the finite--dimensional local Weyl modules and the dual of the infinite--dimensional global Weyl modules respectively. A key step in proving the reciprocity is defining a filtration on the projective modules. Another is relating the characters of the local Weyl modules, which are known, to the characters of global Weyl modules. In the second part, I define the canonical filtration of a graded module for the current algebra. In the case when g is of type A, I show that the well--known homological condition for a canonical filtration to be a costandard filtration also holds in my situation. Finally, using these results, I construct the indecomposable tilting modules in this category and show that any tilting module is isomorphic to a direct sum of indecomposable tilting modules." @default.
- W174945701 created "2016-06-24" @default.
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- W174945701 date "2012-01-01" @default.
- W174945701 modified "2023-09-27" @default.
- W174945701 title "Tilting Modules for the Current Algebra Associated to a Simple Lie Algebra" @default.
- W174945701 hasPublicationYear "2012" @default.
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