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Demazure Modules, Chari–Venkatesh Modules and Fusion Products
Symmetry, integrability and geometry: methods and applications, Tome 10 (2014) Cet article a éte moissonné depuis la source Math-Net.Ru

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Let $\mathfrak{g}$ be a finite-dimensional complex simple Lie algebra with highest root $\theta$. Given two non-negative integers $m$, $n$, we prove that the fusion product of $m$ copies of the level one Demazure module $D(1,\theta)$ with $n$ copies of the adjoint representation $\mathrm{ev}_0 V(\theta)$ is independent of the parameters and we give explicit defining relations. As a consequence, for $\mathfrak{g}$ simply laced, we show that the fusion product of a special family of Chari–Venkatesh modules is again a Chari–Venkatesh module. We also get a description of the truncated Weyl module associated to a multiple of $\theta$.
Keywords: current algebra; Demazure module; Chari–Venkatesh module; truncated Weyl module; fusion product. 
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     author = {Bhimarthi Ravinder},
     title = {Demazure {Modules,} {Chari{\textendash}Venkatesh} {Modules} and {Fusion} {Products}},
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     url = {http://geodesic.mathdoc.fr/item/SIGMA_2014_10_a109/}
}
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Bhimarthi Ravinder. Demazure Modules, Chari–Venkatesh Modules and Fusion Products. Symmetry, integrability and geometry: methods and applications, Tome 10 (2014). http://geodesic.mathdoc.fr/item/SIGMA_2014_10_a109/

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