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The rational Heun operator and Wilson biorthogonal functions
Satoshi Tsujimoto, Luc Vinet, Alexei Zhedanov
We consider the rational Heun operator defined as the most general second-order -difference operator which sends any rational function of type to a rational function…
The dual pair , -oscillators and Askey-Wilson algebras
Luc Frappat, Julien Gaboriaud, Eric Ragoucy +1
The universal Askey-Wilson algebra can be obtained as the commutant of in . We analyze the commutant of $\math…
Dunkl-Supersymmetric Orthogonal functions associated with classical orthogonal polynomials
Yu Luo, Satoshi Tsujimoto, Luc Vinet +1
We consider the eigenvalue problem associated with the Dunkl-type differential operator (in which the reflection operator R is involved) L = dx R + v(x), (v(-x) = -v(x)), in the co…
Truncation of the reflection algebra and the Hahn algebra
Nicolas Crampe, Eric Ragoucy, Luc Vinet +1
In the context of connections between algebras coming from quantum integrable systems and algebras associated to the orthogonal polynomials of the Askey scheme, we prove that the t…
The -Higgs and Askey-Wilson algebras
Luc Frappat, Julien Gaboriaud, Eric Ragoucy +1
A -analogue of the Higgs algebra, which describes the symmetry properties of the harmonic oscillator on the -sphere, is obtained as the commutant of the $\mathfrak{o}_{q^{1/2…
Spin Chains, Graphs and State Revival
Hiroshi Miki, Satoshi Tsujimoto, Luc Vinet
Connections between the 1-excitation dynamics of spin lattices and quantum walks on graphs will be surveyed. Attention will be paid to perfect state transfer (PST) and fractional r…