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Generalized Demazure Modules with Level Two Filtrations

  • Author(s): Davis, Justin Sean 'Tore
  • Advisor(s): Chari, Vyjayanthi
  • et al.

We study generalized Demazure modules over the current algebra $\lie{g} \otimes \mathbb{C}[t]$; or equivalently over the maximal standard parabolic subalgebra in the affine Lie algebra $\widehat{\lie g}$, where $\lie g$ is a finite dimensional complex simple Lie algebra of Type $B$ or $C$. More specifically, for a certain family of pairs of weights, we study generalized Demazure modules as submodules in a tensor product of level one Demazure modules. We give a presentation of these modules, and in the process give an algorithm for computing their graded characters in terms of level two Demazure modules.

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