Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Weight polytopes and saturation of Demazure characters   For $G$ a reductive group and $T\subset B$ a maximal torus and Borel
subgroup, Demazure modules are certain $B$-submodules, indexed by elements of
the Weyl group, of the finite irreducible representations of $G$. In order to
describe the $T$-weight spaces that appear in a Demazure module, we study the
convex hull of these weights - the Demazure polytope. We characterize these
polytopes both by vertices and by inequalities, and we use these results to
prove that Demazure characters are saturated, in the case that $G$ is simple of
classical Lie type. Specializing to $G=GL_n$, we recover results of Fink,
M\'esz\'aros, and St. Dizier, and separately Fan and Guo, on key polynomials,
originally conjectured by Monical, Tokcan, and Yong.

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The categories of this paper are: quant-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: chem-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: alg-geom
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The categories of this paper are: patt-sol
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The categories of this paper are: stat
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The categories of this paper are: q-alg
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The categories of this paper are: math-ph
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The categories of this paper are: nlin
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The categories of this paper are: cs
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The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-bio
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The categories of this paper are: physics