Restriction of the metaplectic representation over a $p$-adic field to an anisotropic torus

In this article, we examine the restriction of the metaplectic representation $π$ over a $p$-adic field $k$, $p\neq2$, of zero characteristic to an isotropic torus $S$ contained in the symplectic group. First we give necessary and sufficient conditions on the momentum map in order that $S$ be admiss