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The Heun-Askey-Wilson algebra and the Heun operator of Askey-Wilson type (1811.11407v2)
Published 28 Nov 2018 in math-ph and math.MP
Abstract: The Heun-Askey-Wilson algebra is introduced through generators ${\boX,\boW}$ 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 $\boW$ 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 $n+1$.