Flag Partial Differential Equations and Representations of Lie Algebras

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dc.creatorXu, Xiaoping
dc.date2007-06-28
dc.date.accessioned2026-07-07T08:13:03Z
dc.date.available2026-07-07T08:13:03Z
dc.descriptionIn this paper, we solve the initial value problems of variable-coefficient generalized wave equations associated with trees and a large family of linear constant-coefficient partial differential equation by algebraic methods. Moreover, we find all the polynomial solutions for a 3-dimensional variable-coefficient flag partial differential equation of any order, the linear wave equation with dissipation and the generalized anisymmetrical Laplace equation. Furthermore, the polynomial-trigonometric solutions of a generalized Klein-Gordan equation associated with 3-dimensional generalized Tricomi operator $\ptl_x^2+x\ptl_y^2+y\ptl_z^2$ are also given. As applications to representations of Lie algebras, we find certain irreducible polynomial representations of the Lie algebras $sl(n,\mbb{F}), so(n,\mbb{F})$ and the simple Lie algebra of type $G_2$.
dc.description30pages
dc.identifierhttps://arxiv.org/abs/0706.4195
dc.identifierhttp://arxiv.org/abs/0706.4195
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/132668
dc.subjectRepresentation Theory
dc.subjectMathematical Physics
dc.subjectAnalysis of PDEs
dc.subjectExactly Solvable and Integrable Systems
dc.titleFlag Partial Differential Equations and Representations of Lie Algebras
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