Physical role of the meta Hahn algebra

Determine whether the meta Hahn algebra, with its distinguished split bases and generalized eigenvalue problem, plays a structural role comparable to that of quadratic Hahn-type algebras in physical superintegrable models.

Background

Quadratic algebras of Hahn type arise as symmetry algebras of superintegrable models and govern associated bispectral problems. The paper identifies the meta Hahn algebra as an algebraic structure with distinguished split bases and a generalized eigenvalue problem, but leaves unresolved whether this structure has a comparable interpretation or function in a physical model.

References

Whether the meta Hahn algebra, with its distinguished split bases and its generalized eigenvalue problem, plays a comparable structural role in a physical setting is a question we find worth asking.

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