Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Polyhedral realizations of crystal bases and convex-geometric Demazure
  operators   The main object in this paper is a certain rational convex polytope whose
lattice points give a polyhedral realization of a highest weight crystal basis.
This is also identical to a Newton-Okounkov body of a flag variety, and it
gives a toric degeneration. In this paper, we prove that a specific class of
this polytope is given by Kiritchenko's Demazure operators on polytopes. This
implies that polytopes in this class are all lattice polytopes. As an
application, we give a sufficient condition for the corresponding toric variety
to be Gorenstein Fano.

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The categories of this paper are: ao-sci
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The categories of this paper are: dg-ga
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The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
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The categories of this paper are: hep-ex
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The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
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The categories of this paper are: bayes-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: quant-ph
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The categories of this paper are: supr-con
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The categories of this paper are: funct-an
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The categories of this paper are: adap-org
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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