Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A class of partition functions associated with $E_{\tau,\eta}(gl_3)$ by
  Izergin-Korepin analysis   Recently, a class of partition functions associated with higher rank rational
and trigonometric integrable models were introduced by Foda and Manabe. We use
the dynamical $R$-matrix of the elliptic quantum group $E_{\tau,\eta}(gl_3)$ to
introduce an elliptic analogue of the partition functions associated with
$E_{\tau,\eta}(gl_3)$. We investigate the partition functions of Foda-Manabe
type by developing a nested version of the elliptic Izergin-Korepin analysis,
and present the explicit forms as symmetrization of multivariable elliptic
functions. We show that special cases are essentially the elliptic weights
functions introduced in the works by Rim\'anyi-Tarasov-Varchenko, Konno,
Felder-Rim\'anyi-Varchenko.

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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: chao-dyn
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The categories of this paper are: cmp-lg
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The categories of this paper are: bayes-an
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The categories of this paper are: alg-geom
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The categories of this paper are: patt-sol
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The categories of this paper are: solv-int
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The categories of this paper are: stat
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The categories of this paper are: q-alg
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The categories of this paper are: q-fin
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The categories of this paper are: funct-an
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The categories of this paper are: plasm-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: ao-sci
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The categories of this paper are: nucl-ex