Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Simplicity of spectra for Bethe subalgebras in $Y(\mathfrak{gl}_2)$   We consider Bethe subalgebras B(C) in the Yangian $Y(\mathfrak{gl}_2)$ with
$C$ regular $2\times 2$ matrix. We study the action of Bethe subalgebras of
$Y(\mathfrak{gl}_2)$ on finite-dimensional representations of
$Y(\mathfrak{gl}_2)$. We prove that $B(C)$ with real diagonal $C$ has simple
spectrum on any irreducible $Y(\mathfrak{gl}_2)$-module corresponding to a
disjoint union of real strings. We extend this result to limits of Bethe
algebras. Our main tool is the computation of Shapovalov-type determinant for
the nilpotent degeneration of $B(C)$.

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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: funct-an
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The categories of this paper are: math-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-th
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The categories of this paper are: adap-org
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The categories of this paper are: comp-gas
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The categories of this paper are: econ
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The categories of this paper are: hep-ph
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The categories of this paper are: nlin
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The categories of this paper are: eess
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The categories of this paper are: gr-qc
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The categories of this paper are: dg-ga