An infinite dimensional algebra denoted A¯ q that is isomorphic to a central extension of U
q+-the positive part of U q (sl 2 ˆ)-has been recently proposed by Paul Terwilliger. It provides …

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 …

We present explicit formulas for the operators providing missing labels for the tensor product
of two irreducible representations of su 3. The result is seen as a particular representation of …

The diagonalization of the Heun–Racah operator is studied with the help of the modified
algebraic Bethe ansatz. This operator is the most general bilinear expression in two …

We introduce Heun algebras of Lie type. They are obtained from bispectral pairs associated
to simple or solvable Lie algebras of dimension three or four. For $\mathfrak {su}(2) $, this …

The centralizer of the image of the diagonal embedding of U_q (sl _2) U q (sl 2) in the tensor
product of three irreducible representations is examined in a Schur–Weyl duality spirit. The …

The Heun–Racah and Heun–Bannai–Ito algebras are introduced. Specializations of these
algebras are seen to be realized by the operators obtained by applying the algebraic Heun …

The time and band limiting operator is introduced to optimize the reconstruction of a signal
from only a partial part of its spectrum. In the discrete case, this operator commutes with the …

The q-difference equation, the shift and the contiguity relations of the Askey–Wilson
polynomials are cast in the framework of the three and four-dimensional degenerate …

The q-Racah polynomials are expressed in terms of certain ratios of scalar products of Bethe
states associated with Bethe equations of either homogeneous or inhomogeneous type …