The HeunAskeyWilson Algebra and the Heun Operator of AskeyWilson Type
Abstract
The HeunAskeyWilson algebra is introduced through generators $\{\boX,\boW\}$ and relations. These relations can be understood as an extension of the usual AskeyWilson ones. A central element is given, and a canonical form of the HeunAskeyWilson algebra is presented. A homomorphism from the HeunAskeyWilson algebra to the AskeyWilson one is identified. On the vector space of the polynomials in the variable $x=z+z^{1}$, the Heun operator of AskeyWilson 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 $n+1$.
 Publication:

Annales Henri Poincaré
 Pub Date:
 September 2019
 DOI:
 10.1007/s00023019008213
 arXiv:
 arXiv:1811.11407
 Bibcode:
 2019AnHP...20.3091B
 Keywords:

 Mathematical Physics;
 33D45;
 16S99
 EPrint:
 16 pages