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

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

2006-06-04

arxiv.org/abs/math/0606085v1

In: Jack, Hall-Littlewood and Macdonald Polynomials (E.B.Kuznetsov and S.Sahi,eds). Amer. Math. Soc., Contemporary Math. vol.

Mathematics

Representation Theory

39 pages, to appear in: "Jack, Hall-Littlewood and Macdonald polynomials", Contemporary Mathematics, AMS

Scientific paper

We 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.

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