Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A crystal to rigged configuration bijection and the filling map for type
  $D_4^{(3)}$   We give a bijection $\Phi$ from rigged configurations to a tensor product of
Kirillov--Reshetikhin crystals of the form $B^{r,1}$ and $B^{1,s}$ in type
$D_4^{(3)}$. We show that the cocharge statistic is sent to the energy
statistic for tensor products $\bigotimes_{i=1}^N B^{r_i,1}$ and
$\bigotimes_{i=1}^N B^{1,s_i}$. We extend this bijection to a single $B^{r,s}$,
show that it preserves statistics, and obtain the so-called
Kirillov--Reshetikhin tableaux model for $B^{r,s}$. Additionally, we show that
$\Phi$ commutes with the virtualization map and that $B^{1,s}$ is naturally a
virtual crystal in type $D_4^{(1)}$, thus defining an affine crystal structure
on rigged configurations corresponding to $B^{1,s}$.

17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
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The categories of this paper are: dg-ga
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The categories of this paper are: plasm-ph
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The categories of this paper are: ao-sci
36
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: funct-an
27
The categories of this paper are: comp-gas
34
The categories of this paper are: chem-ph
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The categories of this paper are: supr-con
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The categories of this paper are: eess
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The categories of this paper are: nucl-th