Structure of invariant subspaces of the rotation group image under the Jordan mapping

We studied the structure of invariant subspaces of effective Hamiltonian of phase light modulation process [1]. Hamiltonian generators satisfy the commutation relationships of SU(2) rotation group [2], thus we can derive their Bose operator representation by using Jordan mapping technique. However, due to the dimensionality of Fock space and additional symmetries of Bose operators, tasks of obtaining eigenbasis, as well as complete classification of invariant subspaces, become nontrivial. In this work, we obtain the relations between the bases of invariant subspaces and derive a classification of the last ones.