Explicit realization of bounded modules for symplectic Lie algebras: spinor versus oscillator

We provide an explicit combinatorial realization of all simple and injective (hence, and projective) modules in the category of bounded sp (2n) -modules. This realization is defined via a natural tableaux correspondence between spinor-type modules of so (2n) and oscillator-type modules of sp (2n). In particular, we show that, in contrast with the A-type case, the generic and bounded sp (2n) -modules admit an analog of the Gelfand-Graev continuation from finite-dimensional representations.