Applications of a Laplace-Beltrami operator for Jack polynomials

作者:Cai, Wuxing*; Jing, Naihuan
来源:European Journal of Combinatorics, 2012, 33(4): 556-571.
DOI:10.1016/j.ejc.2011.11.003

摘要

An explicit computation is made for a Laplace-Beltrami type operator for Jack polynomials. As applications we obtain: combinatorial formula, determinantal formula and raising operator formula for Jack polynomials, as well as an iterative formula for the Littlewood-Richardson coefficients. One special case of our results implies Mimachi-Yamada's result on Jack polynomials of rectangular shapes.