
Journal of Lie Theory 21 (2011), No. 1, 189203 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 [Abstractpdf] \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, MarkovKrein correspondence, spline function, Jack polynomial. MSC: 60B05, 65D07 [ Fulltextpdf (212 KB)] for subscribers only. 