Geodesic
Jack vertex operators and realization of Jack functions
Journal of Algebraic Combinatorics, Tome 39 (2014) no. 1, pp. 53-74.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

We give an iterative method to realize general Jack functions using vertex operators. We first prove some cases of Stanley's conjecture on positivity of the Littlewood-Richardson coefficients, and then use this method to give a new realization of Jack functions. We also show that the images of coefficients of products of Jack vertex operators form a basis of symmetric functions. In particular, this gives a new proof of linear independence for the rectangular and marked rectangular Jack vertex operators. Finally, a generalized Frobenius formula for Jack functions is given and used for evaluation of Dyson integrals and even powers of Vandermonde determinants.
Classification : 05E05, 17B69
Keywords: symmetric functions, Jack polynomials, vertex operators 
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     title = {Jack vertex operators and realization of {Jack} functions},
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Cai, Tommy Wuxing; Jing, Naihuan. Jack vertex operators and realization of Jack functions. Journal of Algebraic Combinatorics, Tome 39 (2014) no. 1, pp. 53-74. http://geodesic.mathdoc.fr/item/JAC_2014__39_1_a7/