Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Minuscule Schubert varieties: Poset polytopes, PBW-degenerated Demazure
  modules, and Kogan faces   We study a family of posets and the associated chain and order polytopes. We
identify the order polytope as a maximal Kogan face in a Gelfand-Tsetlin
polytope of a multiple of a fundamental weight. We show that the character of
such a Kogan face equals to the character of a Demazure module which occurs in
the irreducible representation of $\mathfrak{sl}_n$ having highest weight
multiple of fundamental weight and for any such Demazure module there exists a
corresponding poset and associated maximal Kogan face. We prove that the chain
polytope parametrizes a monomial basis of the associated PBW-graded Demazure
module and further, that the Demazure module is a favourable module, e.g.
interesting geometric properties are governed by combinatorics of convex
polytopes. Thus, we obtain for any minuscule Schubert variety a flat
degeneration into a toric projective variety which is projectively normal and
arithmetically Cohen-Macaulay. We provide a necessary and sufficient condition
on the Weyl group element such that the toric variety associated to the chain
polytope and the toric variety associated to the order polytope are isomorphic.

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The categories of this paper are: funct-an
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The categories of this paper are: solv-int
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The categories of this paper are: dg-ga
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The categories of this paper are: eess
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The categories of this paper are: astro-ph
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The categories of this paper are: supr-con
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The categories of this paper are: econ
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The categories of this paper are: acc-phys
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The categories of this paper are: math-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: ao-sci
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The categories of this paper are: nucl-th
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The categories of this paper are: q-bio
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-ex