Enveloping algebra U(gl(3)) and orthogonal polynomials in several discrete indeterminates

dc.creatorSergeev, Alexander
dc.date2002-02-18
dc.date.accessioned2026-07-07T04:46:33Z
dc.date.available2026-07-07T04:46:33Z
dc.descriptionLet A be an associative complex algebra and L an invariant linear functional on it (trace). Let i be an involutive antiautomorphism of A such that L(i(a))=L(a) for any a in A. Then A admits a symmetric invariant bilinear form (a, b)=L(a i(b)). For A=U(sl(2))/m, where m is any maximal ideal of U(sl(2)), Leites and I have constructed orthogonal basis whose elements turned out to be, essentially, Chebyshev and Hahn polynomials in one discrete variable. Here I take A=U(gl(3))/m for the maximal ideals m which annihilate irreducible highest weight gl(3)-modules of particular form (generalizations of symmetric powers of the identity representation). In this way we obtain multivariable analogs of Hahn polynomials.
dc.description12p., Latex
dc.identifierhttps://arxiv.org/abs/math/0202182
dc.identifierhttp://arxiv.org/abs/math/0202182
dc.identifierDuplij S., Wess J. (eds.) Noncommutative structures in mathematics and physics, Proc. NATO Advanced Research Workshop, Kiev, 2000. Kluwer, 2001, 113--124
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/63373
dc.subjectRepresentation Theory
dc.subject17B10 (Primary) 17B65, 33C45, 33C80 (Secondary)
dc.titleEnveloping algebra U(gl(3)) and orthogonal polynomials in several discrete indeterminates
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