Nature of spin q-Whittaker orthogonality

Determine whether the orthogonality of the inhomogeneous spin q-Whittaker polynomials with respect to the variant of the Sklyanin torus measure arises from the same Bethe Ansatz and self-adjoint-operator structure as the orthogonality of the spin Hall–Littlewood rational functions.

Background

The paper proves that inhomogeneous spin q-Whittaker polynomials are orthogonal under an explicit torus measure. It contrasts this result with the known orthogonality of spin Hall–Littlewood functions, which is connected to their role as a complete family of Bethe Ansatz eigenfunctions for self-adjoint operators, including the XXZ spin-chain Hamiltonian.

Although orthogonality is established for the spin q-Whittaker polynomials, the paper does not identify an analogous spectral or representation-theoretic mechanism. The unresolved issue is therefore whether the two orthogonality results have the same underlying nature.