Highest weight modules over the \(W_{1+\infty}\) algebra and the bispectral problem

DOI10.1215/S0012-7094-98-09302-4zbMath0983.17015arXivq-alg/9602012OpenAlexW2069039605MaRDI QIDQ1974813

Bojko Bakalov, Emil Horozov, Milen T. Yakimov

Publication date: 27 March 2000

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/q-alg/9602012

zbMATH Keywords

representation theoryDarboux transformationbispectral problembispectral operatorBessel tau-functions

Mathematics Subject Classification ID

Virasoro and related algebras (17B68) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35) Correspondences and other transformation methods (e.g., Lie-Bäcklund) for PDEs on manifolds (58J72)

Related Items (11)

Vector orthogonal polynomials with Bochner's property ⋮ Noncommutative bispectral Darboux transformations ⋮ Matrix bispectrality and noncommutative algebras: beyond the prolate spheroidals ⋮ Integral operators, bispectrality and growth of Fourier algebras ⋮ The trigonometric grassmannian and a difference \(W\)-algebra ⋮ Bispectrality of multivariable Racah-Wilson polynomials ⋮ \(\mathcal W\)-symmetry of the adelic Grassmannian ⋮ \(q\)-KP hierarchy, bispectrality and Calogero-Moser systems ⋮ Calogero-Moser spaces and an adelic \(W\)-algebra. ⋮ Fuchsian bispectral operators ⋮ Strictly nilpotent elements and bispectral operators in the Weyl algebra.

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