Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Solitons on Noncommutative Torus as Elliptic Algebras and Elliptic
  Models   For the noncommutative torus ${\cal T}$, in case of the N.C. parameter
$\theta = \frac{Z}{n}$ and the area of ${\cal T}$ is an integer, we construct
the basis of Hilbert space ${\cal H}_n$ in terms of $\theta$ functions of the
positions $z_i$ of $n$ solitons. The loop wrapping around the torus generates
the algebra ${\cal A}_n$. We show that ${\cal A}_n$ is isomorphic to the $Z_n
\times Z_n$ Heisenberg group on $\theta$ functions. We find the explicit form
for the local operators, which is the generators $g$ of an elliptic $su(n)$,
and transforms covariantly by the global gauge transformation of the Wilson
loop in ${\cal A}_n$. By acting on ${\cal H}_n$ we establish the isomorphism of
${\cal A}_n$ and $g$. Then it is easy to give the projection operators
corresponding to the solitons and the ABS construction for generating solitons.
We embed this $g$ into the $L$-matrix of the elliptic Gaudin and C.M. models to
give the dynamics. For $\theta$ generic case, we introduce the crossing
parameter $\eta$ related with $\theta$ and the modulus of ${\cal T}$. The
dynamics of solitons is determined by the transfer matrix $T$ of the elliptic
quantum group ${\cal A}_{\tau, \eta}$, equivalently by the elliptic Ruijsenaars
operators $M$. The eigenfunctions of $T$ found by Bethe ansatz appears to be
twisted by $\eta$.

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The categories of this paper are: bayes-an
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The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
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The categories of this paper are: quant-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: eess
6
The categories of this paper are: astro-ph
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The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
2
The categories of this paper are: math
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The categories of this paper are: funct-an