On the product formula on non-compact Grassmannians

@article{Graczyk2012OnTP,
  title={On the product formula on non-compact Grassmannians},
  author={Piotr Graczyk and Patrice Sawyer},
  journal={arXiv: Representation Theory},
  year={2012}
}
We study the absolute continuity of the convolution $\delta_{e^X}^\natural \star \delta_{e^Y}^\natural$ of two orbital measures on the symmetric space $SO_0(p,q)/SO(p)\timesSO(q)$, $q>p$. We prove sharp conditions on $X$, $Y\in\a$ for the existence of the density of the convolution measure. This measure intervenes in the product formula for the spherical functions. We show that the sharp criterion developed for $\SO_0(p,q)/\SO(p)\times\SO(q)$ will also serve for the spaces $SU(p,q)/S(U(p… 

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