Automorphisms of the Heisenberg–Weyl algebra and d-orthogonal polynomials

DOI10.1063/1.3087425zbMath1202.33018OpenAlexW2022171604MaRDI QIDQ3066497

Luc Vinet, Alexei Zhedanov

Publication date: 11 January 2011

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.3087425

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Connections of hypergeometric functions with groups and algebras, and related topics (33C80) Applications of Lie groups to the sciences; explicit representations (22E70) Other special orthogonal polynomials and functions (33C47)

Related Items (16)

Vector orthogonal polynomials with Bochner's property ⋮ \(d\)-orthogonality and \(q\)-Askey-scheme ⋮ Classes of hypercomplex polynomials of discrete variable based on the quasi-monomiality principle ⋮ Automorphisms of algebras and Bochner's property for vector orthogonal polynomials ⋮ \(d\)-orthogonal polynomials and \(\mathfrak {su}(2)\) ⋮ On \(d\)-orthogonal polynomials with Brenke type generating functions ⋮ On a class of polynomial sets generated by F(xt−R(t)) ⋮ On semi‐classical d‐orthogonal polynomials ⋮ \(C_\lambda\)-extended oscillator algebra and \(d\)-orthogonal polynomials ⋮ A generalization of the symmetric classical polynomials: Hermite and Gegenbauer polynomials ⋮ \(d\)-orthogonal analogs of classical orthogonal polynomials ⋮ Quasi-invariant Hermite polynomials and Lassalle-Nekrasov correspondence ⋮ On connection sequence for equivalent polynomial sets ⋮ q-Oscillator Algebra And d-Orthogonal Polynomials ⋮ Automorphisms of the q-deformed algebra su_q(1, 1) and d-Orthogonal polynomials of q-Meixner type ⋮ On the zeros of some d-orthogonal polynomials

Cites Work

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• Remainder Padé approximants for the exponential function
• Multiple orthogonal polynomials
• Some discrete \(d\)-orthogonal polynomial sets.
• Automorphisms and ideals of the Weyl algebra
• Classical and quantum Heisenberg groups, their representations and applications
• Some discrete multiple orthogonal polynomials
• The relation of the \(d\)-orthogonal polynomials to the Appell polynomials
• Difference equations for discrete classical multiple orthogonal polynomials
• L'orthogonalité et les récurrences de polynômes d'ordre supérieur à deux
• ON A CLASS OF POLYNOMIALS DEFINED BY TWO ORTHOGONALITY RELATIONS
• A generalized hypergeometric d -orthogonal polynomial set
• Some classical multiple orthogonal polynomials

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