Enveloping algebra U(gl(3)) and orthogonal polynomials in several discrete indeterminates
| dc.creator | Sergeev, Alexander | |
| dc.date | 2002-02-18 | |
| dc.date.accessioned | 2026-07-07T04:46:33Z | |
| dc.date.available | 2026-07-07T04:46:33Z | |
| dc.description | 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. | |
| dc.description | 12p., Latex | |
| dc.identifier | https://arxiv.org/abs/math/0202182 | |
| dc.identifier | http://arxiv.org/abs/math/0202182 | |
| dc.identifier | Duplij S., Wess J. (eds.) Noncommutative structures in mathematics and physics, Proc. NATO Advanced Research Workshop, Kiev, 2000. Kluwer, 2001, 113--124 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/63373 | |
| dc.subject | Representation Theory | |
| dc.subject | 17B10 (Primary) 17B65, 33C45, 33C80 (Secondary) | |
| dc.title | Enveloping algebra U(gl(3)) and orthogonal polynomials in several discrete indeterminates | |
| dc.type | text |