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Higher rank classical analogs of the Askey-Wilson algebra from the Onsager algebra
Pascal Baseilhac, Nicolas Crampe, Rodrigo A. Pimenta
The -Onsager algebra has been introduced by Uglov and Ivanov in 1995. In this letter, a FRT presentation of the -Onsager algebra is given, its current algebra and commu…
The Heun-Askey-Wilson algebra and the Heun operator of Askey-Wilson type
Pascal Baseilhac, Satoshi Tsujimoto, Luc Vinet +1
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 ce…
The q-Heun operator of big q-Jacobi type and the q-Heun algebra
Pascal Baseilhac, Luc Vinet, Alexei Zhedanov
The q-Heun operator of the big q-Jacobi type on the exponential grid is defined. This operator is the most general second order q-difference operator that maps polynomials of degre…
FRT presentation of classical Askey-Wilson algebras
Pascal Baseilhac, Nicolas Crampe
Automorphisms of the infinite dimensional Onsager algebra are introduced. Certain quotients of the Onsager algebra are formulated using a polynomial in these automorphisms. In the…
Little and Big Jacobi Polynomials and the Askey-Wilson algebra
Pascal Baseilhac, Xavier Martin, Luc Vinet +1
The little and big q-Jacobi polynomials are shown to arise as basis vectors for representations of the Askey-Wilson algebra. The operators that these polynomials respectively diago…