Jack polynomials and free cumulants
نویسنده
چکیده
We study the coefficients in the expansion of Jack polynomials in terms of power sums. We express them as polynomials in the free cumulants of the transition measure of an anisotropic Young diagram. We conjecture that such polynomials have nonnegative integer coefficients. This extends recent results about normalized characters of the symmetric group. 2000 Mathematics Subject Classification: 05E05, 05E35, 33C52, 46L54.
منابع مشابه
An 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 کاملO ct 2 00 1 CUMULANTS , LATTICE PATHS , AND ORTHOGONAL POLYNOMIALS
A formula expressing free cumulants in terms of the Jacobi parameters of the corresponding orthogonal polynomials is derived. It combines Flajolet's theory of continued fractions and Lagrange inversion. For the converse we discuss Gessel-Viennot theory to express Hankel determinants in terms of various cumulants.
متن کاملRelations between Cumulants in Noncommutative Probability
We express classical, free, Boolean and monotone cumulants in terms of each other, using combinatorics of heaps, pyramids, Tutte polynomials and permutations. We completely determine the coefficients of these formulas with the exception of the formula for classical cumulants in terms of monotone cumulants whose coefficients are only partially computed.
متن کاملOn the computation of classical, boolean and free cumulants
This paper introduces a simple and computationally efficient algorithm for conversion formulae between moments and cumulants. The algorithm provides just one formula for classical, boolean and free cumulants. This is realized by using a suitable polynomial representation of Abel polynomials. The algorithm relies on the classical umbral calculus, a symbolic language introduced by Rota and Taylor...
متن کاملFree Probability and Representations of Large Symmetric Groups
We study the asymptotic behavior of the free cumulants (in the sense of free probability theory of Voiculescu) of Jucys–Murphy elements—or equivalently—of the transition measure associated with a Young diagram. We express these cumulants in terms of normalized characters of the appropriate representation of the symmetric group Sq. Our analysis considers the case when the Young diagrams rescaled...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2009