Limits of BC-type orthogonal polynomials as the number of variables goes to infinity

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dc.creatorOkounkov, Andrei
dc.creatorOlshanski, Grigori
dc.date2006-06-04
dc.date.accessioned2026-07-07T07:37:03Z
dc.date.available2026-07-07T07:37:03Z
dc.descriptionWe describe the asymptotic behavior of the multivariate BC-type Jacobi polynomials as the number of variables and the Young diagram indexing the polynomial go to infinity. In particular, our results describe the approximation of the spherical functions of the infinite-dimensional symmetric spaces of type B,C,D or BC by the spherical functions of the corresponding finite-dimensional symmetric spaces. Similar results for the Jack polynomials were established in our earlier paper (Intern. Math. Res. Notices 1998, no. 13, 641-s682; arXiv:q-alg/9709011). The main results of the present paper were obtained in 1997.
dc.description39 pages, to appear in: "Jack, Hall-Littlewood and Macdonald polynomials", Contemporary Mathematics, AMS
dc.identifierhttps://arxiv.org/abs/math/0606085
dc.identifierhttp://arxiv.org/abs/math/0606085
dc.identifierIn: Jack, Hall-Littlewood and Macdonald Polynomials (E.B.Kuznetsov and S.Sahi,eds). Amer. Math. Soc., Contemporary Math. vol. 417, 2006
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/120646
dc.subjectRepresentation Theory
dc.subjectClassical Analysis and ODEs
dc.subject33C52; 43A90
dc.titleLimits of BC-type orthogonal polynomials as the number of variables goes to infinity
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