Highest weight Macdonald and Jack polynomials
نویسندگان
چکیده
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 کاملMacdonald Polynomials and Geometry
We explain some remarkable connections between the twoparameter symmetric polynomials discovered in 1988 by Macdonald, and the geometry of certain algebraic varieties, notably the Hilbert scheme Hilb(C 2 ) of points in the plane, and the variety Cn of pairs of commuting n× n matrices.
متن کاملReview of “Jack, Hall-Littlewood and Macdonald polynomials”, V. B. Kuznetsov and S. Sahi (eds.)
The book under review contains the Proceedings of a Workshop held in 2003 in Edinburgh, UK. This workshop paid attention to (in fact, celebrated) the pioneering work by the mathematicians Henry Jack, Philip Hall and D. E. Littlewood on two new families of symmetric polynomials, and to the magnificent job done by Ian Macdonald to bring these two classes of polynomials together in a more general ...
متن کاملFactorisation of Macdonald polynomials
1. Macdonald polynomials Macdonald polynomials P λ (x; q, t) are orthogonal symmetric polynomials which are the natural multivariable generalisation of the continuous q-ultraspherical polyno-mials C n (x; β|q) [2] which, in their turn, constitute an important class of hyper-geometric orthogonal polynomials in one variable. Polynomials C n (x; β|q) can be obtained from the general Askey-Wilson p...
متن کاملMacdonald Polynomials and Algebraic Integrability
We construct explicitly (non-polynomial) eigenfunctions of the difference operators by Macdonald in case t = q, k ∈ Z. This leads to a new, more elementary proof of several Macdonald conjectures, first proved by Cherednik. We also establish the algebraic integrability of Macdonald operators at t = q (k ∈ Z), generalizing the result of Etingof and Styrkas. Our approach works uniformly for all ro...
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ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and Theoretical
سال: 2011
ISSN: 1751-8113,1751-8121
DOI: 10.1088/1751-8113/44/5/055204