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- W2890525403 abstract "Author(s): Murray, Kayla | Advisor(s): Chari, Vyjayanthi | Abstract: For a simple Lie algebra $mathfrak{g}$ over $mathbb{C},$ we study the representations of the associated current algebra $mathfrak{g}[t].$ We focus our attention on $V(boldsymbol xi)$ modules, which are a large family of indecomposable representations that are quotients of local Weyl modules and include Demazure modules when $mathfrak{g}$ is simply laced. We establish three new presentations of $V(boldsymbol xi)$ modules, which show that they are finitely presented as quotients of local Weyl modules. We establish each presentation for $mathfrak{sl}_2$ and then for an arbitrary $mathfrak{g}.$ With these presentations, we establish the existence of two short exact sequences of $V(boldsymbol xi)$ modules. These short exact sequences were used to establish a character formula for the tensor product of a level 2 Demazure module and a local Weyl module." @default.
- W2890525403 created "2018-09-27" @default.
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- W2890525403 date "2018-01-01" @default.
- W2890525403 modified "2023-09-23" @default.
- W2890525403 title "Graded Representations of Current Algebras" @default.
- W2890525403 hasPublicationYear "2018" @default.
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