LU-decomposition of a noncommutative linear system and Jacobi polynomials

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dc.creatorBrega, Alfredo
dc.creatorCagliero, Leandro
dc.date2008-10-15
dc.date.accessioned2026-07-07T10:10:27Z
dc.date.available2026-07-07T10:10:27Z
dc.descriptionIn this paper we obtain the LU-decomposition of a noncommutative linear system of equations that, in the rank one case, characterizes the image of the Lepowsky homomorphism $U(\lieg)^{K}\to U(\liek)^{M}\otimes U(\liea)$. This LU-decomposition can be transformed into very simple matrix identities, where the entries of the matrices involved belong to a special class of Jacobi polynomials. In particular, each entry of the L part of the original system is expressed in terms of a single ultraspherical Jacobi polynomial. In turns, these matrix identities yield a biorthogonality relation between the ultraspherical Jacobi polynomials.
dc.identifierhttps://arxiv.org/abs/0810.2771
dc.identifierhttp://arxiv.org/abs/0810.2771
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/171607
dc.subjectRepresentation Theory
dc.subjectCombinatorics
dc.subject33C45; 22E46; 15A23; 15A54
dc.titleLU-decomposition of a noncommutative linear system and Jacobi polynomials
dc.typetext

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