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Mathematics > Representation Theory

arXiv:math/0202182 (math)
[Submitted on 18 Feb 2002]

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

Authors:Alexander Sergeev (University of Stockholm)
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Abstract: Let 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.
Comments: 12p., Latex
Subjects: Representation Theory (math.RT)
MSC classes: 17B10 (Primary) 17B65, 33C45, 33C80 (Secondary)
Cite as: arXiv:math/0202182 [math.RT]
  (or arXiv:math/0202182v1 [math.RT] for this version)
  https://doi.org/10.48550/arXiv.math/0202182
Journal reference: Duplij S., Wess J. (eds.) Noncommutative structures in mathematics and physics, Proc. NATO Advanced Research Workshop, Kiev, 2000. Kluwer, 2001, 113--124

Submission history

From: Dimitry Leites [view email]
[v1] Mon, 18 Feb 2002 19:33:04 UTC (13 KB)
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