منابع مشابه
Asymptotics of Characters of Symmetric Groups and Free Probability
In order to answer the question “what is the asymptotic theory of representations of Sn” we will present two concrete problems. In both cases the solution requires a good understanding of the product (convolution) of conjugacy classes in the symmetric group and we will present a combinatorial setup for explicit calculation of such products. The asymptotic behavior of each summand in our expansi...
متن کاملAsymptotics of Jack Polynomials as the Number of Variables Goes to Infinity
In this paper we study the asymptotic behavior of the Jack rational functions Pλ(z1, . . . , zn; θ) as the number of variables n and the signature λ grow to infinity. Our results generalize the results of A. Vershik and S. Kerov [VK2] obtained in the Schur function case (θ = 1). For θ = 1/2, 2 our results describe approximation of the spherical functions of the infinite-dimensional symmetric sp...
متن کاملAn Identity of Jack Polynomials
In this work we give an alterative proof of one of basic properties of zonal polynomials and generalised it for Jack polynomials
متن کاملAsymptotics of characters of symmetric groups: Structure of Kerov character polynomials
We study asymptotics of characters of the symmetric groups on a fixed conjugacy class. It was proved by Kerov that such a character can be expressed as a polynomial in free cumulants of the Young diagram (certain functionals describing the shape of the Young diagram). We show that for each genus there exists a universal symmetric polynomial which gives the coefficients of the part of Kerov char...
متن کاملAsymptotics of characters of symmetric groups, Gaussian fluctuations of Young diagrams and genus expansion
The convolution of indicators of two conjugacy classes on the symmetric group Sq is usually a complicated linear combination of indicators of many conjugacy classes. Similarly, a product of the moments of the Jucys–Murphy element involves many conjugacy classes with complicated coefficients. In this article we consider a combinatorial setup which allows us to manipulate such products easily: to...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2019
ISSN: 0097-3165
DOI: 10.1016/j.jcta.2019.02.020