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
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In the 1920’s, Ritt studied the operation of functional composition g ◦ h(x) = g(h(x)) on complex rational functions. In the case of polynomials, he described all the ways in which a polynomial can have multiple ‘prime factorizations’ with respect to this operation. Despite significant effort by Ritt and others, little progress has been made towards solving the analogous problem for rational fu...
متن کاملMultivariate Positive Laurent Polynomials
Recently Dritschel proves that any positive multivariate Laurent polynomial can be factorized into a sum of square magnitudes of polynomials. We first give another proof of the Dritschel theorem. Our proof is based on the univariate matrix Féjer-Riesz theorem. Then we discuss a computational method to find approximates of polynomial matrix factorization. Some numerical examples will be shown. F...
متن کاملAverages of ratios of characteristic polynomials in circular β-ensembles and super-Jack polynomials
We study the averages of ratios of characteristic polynomials over circular β-ensembles, where β is a positive real number. Using Jack polynomial theory, we obtain three expressions for ratio averages. Two of them are given as sums of super-Jack polynomials and another one is given by a hyperdeterminant. As applications, we give dualities for ratio averages between β and 4/β. MSC-class: primary...
متن کاملJack polynomials in superspace
This work initiates the study of orthogonal symmetric polynomials in superspace. Here we present two approaches leading to a family of orthogonal polynomials in superspace that generalize the Jack polynomials. The first approach relies on previous work by the authors in which eigenfunctions of the supersymmetric extension of the trigonometric Calogero-Moser-Sutherland Hamiltonian were construct...
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ژورنال
عنوان ژورنال: Algebras and Representation Theory
سال: 2018
ISSN: 1386-923X,1572-9079
DOI: 10.1007/s10468-018-9778-4