Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Decorated Geometric Crystals, Polyhedral and Monomial Realizations of
  Crystal Bases   We shall show that for type $A_n$ the realization of crystal bases obtained
from the decorated geometric crystals intorduced by Berenstein and Kazhdan
coincides with our polyhedral realizations of crystal bases. We also observe
certain relations of decorations and monomial realizations of crystal bases.

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The categories of this paper are: hep-ph
24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
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The categories of this paper are: patt-sol
29
The categories of this paper are: funct-an
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-ex