Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Soliton cellular automaton associated with $G_2^{(1)}$ crystal base   We calculate the combinatorial $R$ matrix for all elements of
$\mathcal{B}_l\otimes \mathcal{B}_1$ where $\mathcal{B}_l$ denotes the
$G_2^{(1)}$-perfect crystal of level $l$, and then study the soliton cellular
automaton constructed from it. The solitons of length $l$ are identified with
elements of the $A_1^{(1)}$-crystal $\tilde{\mathcal{B}}_{3l}$. The scattering
rule for our soliton cellular automaton is identified with the combinatorial
$R$ matrix for $A_1^{(1)}$-crystals.

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The categories of this paper are: q-alg
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
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The categories of this paper are: solv-int
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The categories of this paper are: comp-gas
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The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex