Journal of Lie Theory

no. 1
Dirichlet Distribution and Orbital Measures
Journal of Lie Theory, Volume 21 (2011) no. 1, pp. 189-203
\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.
DOI: 10.5802/jolt.629
Classification: 60B05, 65D07
Keywords: Dirichlet distribution, orbital measure, Markov-Krein correspondence, spline function, Jack polynomial 
@article{JOLT_2011_21_1_a8,
     author = {F. Fourati},
     title = {Dirichlet {Distribution} and {Orbital} {Measures}},
     journal = {Journal of Lie Theory},
     pages = {189--203},
     year = {2011},
     volume = {21},
     number = {1},
     doi = {10.5802/jolt.629},
     zbl = {1229.60008},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.629/}
}
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F. Fourati. Dirichlet Distribution and Orbital Measures. Journal of Lie Theory, Volume 21 (2011) no. 1, pp. 189-203. doi: 10.5802/jolt.629

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