Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The $BC_{1}$ Elliptic model: algebraic forms, hidden algebra $sl(2)$,
  polynomial eigenfunctions   The potential of the $BC_1$ quantum elliptic model is a superposition of two
Weierstrass functions with doubling of both periods (two coupling constants).
The $BC_1$ elliptic model degenerates to $A_1$ elliptic model characterized by
the Lam\'e Hamiltonian. It is shown that in the space of $BC_1$ elliptic
invariant, the potential becomes a rational function, while the flat space
metric becomes a polynomial. The model possesses the hidden $sl(2)$ algebra for
arbitrary coupling constants: it is equivalent to $sl(2)$-quantum top in three
different magnetic fields. It is shown that there exist three one-parametric
families of coupling constants for which a finite number of polynomial
eigenfunctions (up to a factor) occur.

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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
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The categories of this paper are: stat
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The categories of this paper are: hep-lat
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The categories of this paper are: econ
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The categories of this paper are: gr-qc
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The categories of this paper are: astro-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: q-bio
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The categories of this paper are: acc-phys