  This article is a contribution to the domain of (convergent) deformation
quantization of symmetric spaces by use of Lie groups representation theory. We
realize the regular representation of $SL(2,\R)$ on the space of smooth
functions on the Poincar\'e disc as a sub-representation of $SL(2,\R)$ in the
Weyl-Moyal star product algebra on $\R^2$. We indicate how it is possible to
extend our construction to the general case of a Hermitian symmetric space of
tube type.
