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Is every spin group $Spin(n,R)$ over the reals contained in some metaplectic group $Mp(m,R)$ for some $m$ in such a way that the spin representation is obtained by restriction of the metaplectic representation?
Is every spin group $Spin(n,R)$ over the reals contained in some metaplectic group $Mp(m,R)$ for some $m$?
Is every spin group $Spin(n,R)$ over the reals contained in some metaplectic group $Mp(m,R)$ for some $m$ in such a way that the spin representation is obtained by restriction of the metaplectic representation?
