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Projections of orbital measures for the action of a pseudo-unitary group

Volume 113 / 2017

Jacques Faraut Banach Center Publications 113 (2017), 111-121 MSC: 15A18; 22E15. DOI: 10.4064/bc113-0-7

Abstract

The pseudo-unitary group $U(p,q)$ acts on the space ${\rm Herm}(n,\mathbb{C})$ of $n\times n$ Hermitian matrices ($n=p+q$). For an orbit of convex type we study the projection of the orbit on the subspace ${\rm Herm}(n-1,\mathbb{C})$ and the projection of the associated orbital measure. By using an explicit formula for the Fourier–Laplace transform of such an orbital measure due to Ben Saïd and Ørsted (2005), we prove an analogue of a formula due to Baryshnikov (2001), which is related to the action of the unitary group $U(n)$.

Authors

  • Jacques FarautInstitut de Mathématiques de Jussieu
    Université Pierre et Marie Curie
    4 place Jussieu, case 247
    75252 Paris cedex 05, France
    e-mail

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