Coherent states for the harmonic oscillator representations of the orthosymplectic supergroup Osp(1/2N,R)

Coherent states for the harmonic oscillator representations of the noncompact supergroup Osp(1/2N,$\mathfrak{R}$ ) are introduced and the invariant integration measure is calculated by studying transformation properties of supercoset variables. The generalized Bogoliubov transformation for mixed systems of bosons and fermions is also obtained. An example for the simple harmonic oscillator is given.