Some combinatorial properties of Jack symmetric functions

Advances in Mathematics - Tập 77 - Trang 76-115 - 1989
Richard P Stanley1
1Department of Mathematics, Massachusetts Institute of Technology Cambridge, Massachusetts 02139, USA

Tài liệu tham khảo

Constantine, 1963, Some noncentral distribution problems in multivariate analysis, Ann. Math. Statist., 34, 1270, 10.1214/aoms/1177703863 P. Diaconis and E. Lander, Some formulas for zonal polynomials, in preparation. Foulkes, 1974, A survey of some combinatorial aspects of symmetric functions Hanlon, 1988, Jack symmetric functions and some combinatorial properties of Young symmetrizers, J. Combin. Theory Ser. A, 47, 37, 10.1016/0097-3165(88)90042-8 Jack, 1969, A class of symmetric polynomials with a parameter, 69, 1 James, 1961, Zonal polynomials of the real positive definite symmetric matrices, Ann. of Math., 74, 456, 10.2307/1970291 James, 1964, Distributions of matrix variables and latent roots derived from normal samples, Ann. Math. Statist., 35, 475, 10.1214/aoms/1177703550 James, 1968, Calculation of zonal polynomial coefficients by use of the Laplace-Beltrami operator, Ann. Math. Statist., 39, 1711, 10.1214/aoms/1177698153 H. B. Kushner, The linearization of the product of two zonal polynomials, preprint. Kerber, 1983, Symmetrieklassen von Funktionen und ihre Abzählungstheorie, Bayreuther Mathematische Schriften Littlewood, 1950 Macdonald, 1979 Macdonald, 1987, Commuting differential equations and zonal spherical functions, Vol. 1271, 189 [M3]I. G. Macdonald, [M1], 2nd ed., to appear. Specht, 1960, Die Characktere der symmetrichen Gruppe, Math. Zeit., 73, 312, 10.1007/BF01215313 Takemura, 1984, Zonal Polynomials, Vol. 4