Journal Home Page Cumulative Index List of all Volumes Complete Contentsof this Volume Previous Article Journal of Lie Theory 21 (2011), No. 1, 189--203 Copyright Heldermann Verlag 2011 Dirichlet Distribution and Orbital Measures Faïza Fourati Department of Mathematics, Preparatory Institute of Engineering Studies, University of Tunis, 1089 Monfleury - Tunis, Tunisia fayza.fourati@ipeit.rnu.tn [Abstract-pdf] \def\C{{\Bbb C}} \def\F{{\Bbb F}} \def\R{{\Bbb R}} \def\HH{{\Bbb H}} The starting point of this paper is an observation by Okounkov concerning the projection of orbital measures for the action of the unitary group $U(n)$ on the space Herm$(n,\C)$ of $n\times n$ Hermitian matrices. The projection of such an orbital measure on the straight line generated by a rank one Hermitian matrix is a probability measure whose density is a spline function. More generally we consider the projection of orbital measures for the action of the group $U(n,\F)$ on the space Herm$(n,\F)$ for $\F=\R$, $\C$, $\HH$, and their relation with Dirichlet distributions. Keywords: Dirichlet distribution, orbital measure, Markov-Krein correspondence, spline function, Jack polynomial. MSC: 60B05, 65D07 [ Fulltext-pdf  (212  KB)] for subscribers only.