Projections of orbital measures for the action of a pseudo-unitary group
Volume 113 / 2017
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 $U(n)$.
