Two-diagonal representations of meta Racah and meta Wilson algebras

Determine whether meta Racah and meta Wilson algebras admit two-diagonal representations on the space of sequences that produce the same dual pair of outcomes as the meta Hahn algebra, namely bispectral orthogonal polynomials and biorthogonal rational functions.

Background

The paper classifies two-diagonal representations of the meta Hahn algebra on an infinite-dimensional sequence space and shows that these representations simultaneously yield continuous Hahn-type orthogonal polynomials and biorthogonal rational functions. It then asks whether analogous representation-theoretic constructions exist for higher members of the Racah and Wilson hierarchy, with the same paired spectral consequences.

References

One may also ask how far up the scheme the construction goes, that is, whether meta algebras of Racah and of Wilson type admit two-diagonal representations on the space of sequences with the same dual pair of outcomes.

— Continuous representations of the meta Hahn algebra and special functions  (2610.21494 - Labriet et al., 15 Oct 2026) in Section Outlook