Limits of BC-type orthogonal polynomials as the number of variables goes to infinity
Andrei Okounkov, Grigori Olshanski
Abstract
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.
Create a lesson
Related papers
Noncommutative Cluster Varieties and Moduli Spaces of Local Systems
Zachary Greenberg, Dani Kaufman, Merik Niemeyer et al.
The Saito determinant for extended affine Weyl discriminant strata
Andrea Brini, Karoline van Gemst
Unitary Shimura Correspondence for Complex Classical Groups
Wan-Yu Tsai, Kayue Daniel Wong, Hongfeng Zhang
An enhanced Helgason-Johnson bound for Sp(p, q)
Zhan Ying, Chao-Ping Dong
Auslander-Reiten (n+2)-angles and local finiteness
Jian He, Yu-Zhe Liu, Panyue Zhou
A σ-McKay theorem for π-separable groups
David Cabrera-Berenguer