Papers by Dounia Kabakibo
The missing label for basis vectors of SU(3) representations corresponding to the reduction SU(3)... more The missing label for basis vectors of SU(3) representations corresponding to the reduction SU(3) ⊃ SO(3) can be provided by the eigenvalues of SO(3) scalars in the enveloping algebra of su(3). There are only two such independent elements of degree three and four. It is shown how the one of degree four can be diagonalized using the analytical Bethe ansatz.
Reviews in Mathematical Physics, 2020
The Askey–Wilson algebra is realized in terms of the elements of the quantum algebras [Formula: s... more The Askey–Wilson algebra is realized in terms of the elements of the quantum algebras [Formula: see text] or [Formula: see text]. A new realization of the Racah algebra in terms of the Lie algebras [Formula: see text] or [Formula: see text] is also given. Details for different specializations are provided. The advantage of these new realizations is that one generator of the Askey–Wilson (or Racah) algebra becomes diagonal in the usual representation of the quantum algebras whereas the second one is tridiagonal. This allows us to recover easily the recurrence relations of the associated orthogonal polynomials of the Askey scheme. These realizations involve rational functions of the Cartan generator of the quantum algebras, where they are linear with respect to the other generators and depend on the Casimir element of the quantum algebras.
Journal of Mathematical Physics, 2021
The generic Heun operator of Lie type is identified as a certain BC-Gaudin magnet Hamiltonian in ... more The generic Heun operator of Lie type is identified as a certain BC-Gaudin magnet Hamiltonian in a magnetic field. By using the modified algebraic Bethe ansatz introduced to diagonalize such Gaudin models, we obtain the spectrum of the generic Heun operator of Lie type in terms of the Bethe roots of inhomogeneous Bethe equations. We also show that these Bethe roots are intimately associated with the roots of polynomial solutions of the differential Heun equation. We illustrate the use of this approach in two contexts: the representation theory of O(3) and the computation of the entanglement entropy for free Fermions on the Krawtchouk chain.
International Journal of Modern Physics A
The missing label for basis vectors of [Formula: see text] representations corresponding to the r... more The missing label for basis vectors of [Formula: see text] representations corresponding to the reduction [Formula: see text] can be provided by the eigenvalues of [Formula: see text] scalars in the enveloping algebra of [Formula: see text]. There are only two such independent elements of degrees three and four. It is shown how the one of degree four can be diagonalized using the analytical Bethe ansatz.
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Papers by Dounia Kabakibo