Lie-algebraic approach to the theory of polynomial solutions. I. Ordinary differential equations and finite-difference equations in one variable

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dc.creatorTurbiner, Alexander
dc.date1992-09-22
dc.date.accessioned2026-07-07T09:13:57Z
dc.date.available2026-07-07T09:13:57Z
dc.descriptionA classification of ordinary differential equations and finite-difference equations in one variable having polynomial solutions (the generalized Bochner problem) is given. The method used is based on the spectral problem for a polynomial element of the universal enveloping algebra of $sl_2({\bf R})$ (for differential equations) or $sl_2({\bf R})_q$ (for finite-difference equations) in the "projectivized" representation possessing an invariant subspace. Connection to the recently-discovered quasi-exactly-solvable problems is discussed.
dc.description19pp
dc.identifierhttps://arxiv.org/abs/hep-th/9209079
dc.identifierhttp://arxiv.org/abs/hep-th/9209079
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/152507
dc.subjectHigh Energy Physics - Theory
dc.subjectAlgebraic Geometry
dc.subjectFunctional Analysis
dc.titleLie-algebraic approach to the theory of polynomial solutions. I. Ordinary differential equations and finite-difference equations in one variable
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