Differential Equations for Singular Vectors of sl(n)

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dc.creatorXu, Xiaoping
dc.date2003-05-13
dc.date.accessioned2026-07-07T04:57:57Z
dc.date.available2026-07-07T04:57:57Z
dc.descriptionGiven a weight of sl(n), we derive a system of variable-coefficient second-order linear partial differential equations that determines the singular vectors in the corresponding Verma module. Moreover, we completely solve the system in a certain space of power series. The polynomial solutions correspond to the singular vectors in the Verma module. The well-known results of Verma, Bernstein-Gel'fand-Gel'fand and Jantzen for the case of $sl(n)$ are naturally included in our almost elementary approach of partial differential equations.
dc.description25pages
dc.identifierhttps://arxiv.org/abs/math/0305180
dc.identifierhttp://arxiv.org/abs/math/0305180
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/67447
dc.subjectQuantum Algebra
dc.subjectAnalysis of PDEs
dc.subjectRepresentation Theory
dc.subject17B69
dc.titleDifferential Equations for Singular Vectors of sl(n)
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