A formula for Jack polynomials
 of the second order

Francisco J. Caro-Lopera; José A. Díaz-García; Graciela González-Farías

doi:10.4064/am34-1-9

Instytut Matematyczny Polskiej Akademii Nauk / Institute of Mathematics / Publishing house / Journals and Serials / Applicationes Mathematicae / All issues

A formula for Jack polynomials of the second order

Volume 34 / 2007

Francisco J. Caro-Lopera, José A. Díaz-García, Graciela González-Farías Applicationes Mathematicae 34 (2007), 113-119 MSC: 05E05, 35M99, 33C05. DOI: 10.4064/am34-1-9

Abstract

This work solves the partial differential equation for Jack polynomials $C_{\kappa }^{\alpha }$ of the second order. When the parameter $\alpha$ of the solution takes the values $1/2, 1$ and $2$ we get explicit formulas for the quaternionic, complex and real zonal polynomials of the second order, respectively.

Authors

Francisco J. Caro-LoperaDepartment of Basic Mathematics
Centro de Investigación en Matemáticas
Callejón de Jalisco s//n
Mineral de Valenciana
36240 Guanajuato, Guanajuato, México
e-mail
José A. Díaz-GarcíaDepartment of Statistics and Computation
Universidad Autónoma Agraria Antonio Narro
25315 Buenavista Saltillo, Coahuila, México
e-mail
Graciela González-FaríasDepartment of Statistics
Centro de Investigación en Matemáticas
Callejón de Jalisco s//n
Mineral de Valenciana
36240 Guanajuato, Guanajuato, México
e-mail

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