Lie-algebraic approach to the theory of polynomial solutions. II. Differential equations in one real and one Grassmann variables and 2x2 matrix differential equations

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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 theorem for linear differential equations in two variables (one real and one Grassmann) having polynomial solutions(the generalized Bochner problem) is given. The main result is based on the consideration of the eigenvalue problem for a polynomial element of the universal enveloping algebra of the algebra $osp(2,2)$ in the "projectivized" representation (in differential operators of the first order) possessing an invariant subspace. A classification of 2 x 2 matrix differential equations in one real variable possessing polynomial solutions is described. Connection to the recently-discovered quasi-exactly-solvable problems is discussed.
dc.description24pp
dc.identifierhttps://arxiv.org/abs/hep-th/9209080
dc.identifierhttp://arxiv.org/abs/hep-th/9209080
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/152508
dc.subjectHigh Energy Physics - Theory
dc.subjectAlgebraic Geometry
dc.subjectFunctional Analysis
dc.titleLie-algebraic approach to the theory of polynomial solutions. II. Differential equations in one real and one Grassmann variables and 2x2 matrix differential equations
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