Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Diagonalization of the Heun-Askey-Wilson operator, Leonard pairs and the
  algebraic Bethe ansatz   An operator of Heun-Askey-Wilson type is diagonalized within the framework of
the algebraic Bethe ansatz using the theory of Leonard pairs. For different
specializations and the generic case, the corresponding eigenstates are
constructed in the form of Bethe states, whose Bethe roots satisfy Bethe ansatz
equations of homogeneous or inhomogenous type. For each set of Bethe equations,
an alternative presentation is given in terms of `symmetrized' Bethe roots.
Also, two families of on-shell Bethe states are shown to generate two explicit
bases on which a Leonard pair acts in a tridiagonal fashion. In a second part,
the (in)homogeneous Baxter T-Q relations are derived. Certain realizations of
the Heun-Askey-Wilson operator as second q-difference operators are introduced.
Acting on the Q-polynomials, they produce the T-Q relations. For a special
case, the Q-polynomial is identified with the Askey-Wilson polynomial, which
allows one to obtain the solution of the associated Bethe ansatz equations. The
analysis presented can be viewed as a toy model for studying integrable models
generated from the Askey-Wilson algebra and its generalizations. As examples,
the q-analog of the quantum Euler top and various types of three-sites
Heisenberg spin chains in a magnetic field with inhomogeneous couplings,
three-body and boundary interactions are solved. Numerical examples are given.
The results also apply to the time-band limiting problem in signal processing.

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The categories of this paper are: stat
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
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The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: q-alg
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The categories of this paper are: plasm-ph
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The categories of this paper are: eess
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The categories of this paper are: solv-int
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The categories of this paper are: physics
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The categories of this paper are: q-bio
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The categories of this paper are: cmp-lg
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The categories of this paper are: cond-mat
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The categories of this paper are: q-fin