5 papers
The dynamical algebra of the generic superintegrable model on the two-sphere
Nicolas Crampé, Quentin Labriet, Lucia Morey +3
The rank two Jacobi algebra is identified as the dynamical algebra of the generic quadratic superintegrable model on the two-sphere. The physical representation of…
Meta Algebras and Special Functions: the Racah Case
Nicolas Crampé, Quentin Labriet, Lucia Morey +3
Finite families of biorthogonal rational functions and orthogonal polynomials of Racah-type are studied within a unified algebraic framework based on the meta Racah algebra and its…
Ruijsenaars-van Diejen-Takemura Hamiltonians as rational Heun operators
Satoshi Tsujimoto, Luc Vinet, Alexei Zhedanov
The most general Ruijsenaars-van Diejen-Takemura Hamiltonians are characterized as Heun operators defined as second order -difference operators with a raising action on elementa…
Cauchy-Jacobi orthogonal polynomials and the discrete CKP equation
Shi-Hao Li, Satoshi Tsujimoto, Ryoto Watanabe +1
This paper intends to construct discrete spectral transformations for Cauchy-Jacobi orthogonal polynomials, and find its corresponding discrete integrable systems. It turns out tha…
Discretization of Camassa-Holm peakon equation using orthogonal polynomials and matrix transformations
R. Watanabe, M. Iwasaki, S. Tsujimoto
Discrete integrable systems are closely related to orthogonal polynomials and isospectral matrix transformations. In this paper, we use these relationships to propose a nonautonomo…