The Heun-Askey-Wilson Algebra and the Heun Operator of Askey-Wilson Type

摘要

The Heun-Askey-Wilson algebra is introduced through generators {X, W} and relations. These relations can be understood as an extension of the usual Askey-Wilson ones. A central element is given, and a canonical form of the Heun-Askey-Wilson algebra is presented. A homomorphism from the Heun-Askey-Wilson algebra to the Askey-Wilson one is identified. On the vector space of the polynomials in the variable x = z + z(-1), the Heun operator of Askey-Wilson type realizing W can be characterized as the most general second-order q-difference operator in the variable z that maps polynomials of degree n in x = z + z(-1) into polynomials of degree n + 1.