Orthogonal polynomials of a discrete variable and Lie algebras of matrices of complex order

DOI10.1007/BF02551394zbMath1017.17021arXivmath/0509528OpenAlexW2067147026MaRDI QIDQ1592121

Dimitry Leites, Alexander Sergeev

Publication date: 1 September 2003

Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0509528

zbMATH Keywords

orthogonal polynomialsreal formsLie superalgebrasquasi-finite modulesChebyshev and Hahn \(q\)-polynomialcontinuous Chebyshev and Hahn orthogonal polynomialsFeigin Lie algebraunitarity conditions

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Infinite-dimensional Lie (super)algebras (17B65) Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15)

Related Items (5)

Algebra gl(λ) Inside the Algebra of Differential Operators on the Real Line ⋮ Jacobson generators, Fock representations and statistics of sl(n+1) ⋮ Unnamed Item ⋮ Non-degenerate invariant (super)symmetric bilinear forms on simple Lie (super)algebras ⋮ Sylvester-'t Hooft generators and relations between them for \(\mathfrak{sl}(n)\) and \(\mathfrak{gl}(n| n)\)

Cites Work

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• Extensions of Laguerre operators in indefinite inner product spaces
• Quasifinite highest weight modules over the Lie algebra of differential operators on the circle
• Constructing simple Lie superalgebras from associative graded algebras
• Orthogonal polynomials and singular Sturm-Liouville systems. I
• Quotients simples de l'algèbre enveloppante de \({\mathfrak sl}_2\)
• The Lie algebras $ \mathfrak{gl}(\lambda)$ and cohomologies of Lie algebras of differential operators

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