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Эта публикация цитируется в 10 научных статьях (всего в 10 статьях)
Vector-Valued Jack Polynomials from Scratch
Charles F. Dunkla, Jean-Gabriel Luqueb a Dept. of Mathematics, University of Virginia, Charlottesville VA 22904-4137, USA
b Université de Rouen, LITIS Saint-Etienne du Rouvray, France
Аннотация:
Vector-valued Jack polynomials associated to the symmetric group $\mathfrak S_N$ are polynomials with
multiplicities in an irreducible module of $\mathfrak S_N$ and which are simultaneous eigenfunctions of the Cherednik–Dunkl operators with some additional properties concerning the leading monomial. These polynomials were introduced by Griffeth in the general setting of the complex reflections groups $G(r,p,N)$ and studied by one of the authors (C. Dunkl) in the specialization $r=p=1$ (i.e. for the symmetric group).
By adapting a construction due to Lascoux, we describe an algorithm allowing us to compute explicitly the Jack polynomials following a Yang–Baxter graph. We recover some properties already studied by C. Dunkl
and restate them in terms of graphs together with additional new results. In particular, we investigate normalization, symmetrization and antisymmetrization, polynomials with minimal degree, restriction
etc. We give also a shifted version of the construction and we discuss vanishing properties of the associated
polynomials.
Ключевые слова:
Jack polynomials; Yang–Baxter graph; Hecke algebra.
Поступила: 21 сентября 2010 г.; в окончательном варианте 11 марта 2011 г.; опубликована 16 марта 2011 г.
Образец цитирования:
Charles F. Dunkl, Jean-Gabriel Luque, “Vector-Valued Jack Polynomials from Scratch”, SIGMA, 7 (2011), 026, 48 pp.
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/sigma584 https://www.mathnet.ru/rus/sigma/v7/p26
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