An algebraic interpretation of the intertwining operators associated with the discrete Fourier transform

Abstract

We show that intertwining operators for the discrete Fourier transform form a cubic algebra Cq with q a root of unity. This algebra is intimately related to the two other well-known realizations of the cubic algebra: the Askey-Wilson algebra and the Askey-Wilson-Heun algebra.

An explanation of the commuting operator "miracle" in time and band limiting

“…Finally, one expects that our results could also be derived using a more algebraic approach. Such a derivation would connect to the existing literature on the relation between the finite Fourier transform and the Heun operator, and on their associated bispectral pair in continuous and discrete settings [7,1].…”