Asymptotics of Jack polynomials as the number of variables goes to infinity

Details Asymptotics of Jack polynomials as the number of variables goes to infinity Asymptotics of Jack polynomials as the number of variables goes to infinity

1997-09-05

arxiv.org/abs/q-alg/9709011v1

Intern. Math. Research Notices 1998, no. 13, 641-682

Physics

Condensed Matter

37 pages, AMS TeX

Scientific paper

In this paper we study the asymptotic behavior of the Jack rational functions as the number of variables grows to infinity. Our results generalize the results of A. Vershik and S. Kerov obtained in the Schur function case (theta=1). For theta=1/2,2 our results describe approximation of the spherical functions of the infinite-dimensional symmetric spaces $U(\infty)/O(\infty)$ and $U(2\infty)/Sp(\infty)$ by the spherical functions of the corresponding finite-dimensional symmetric spaces.

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