Model representations for systems of selfadjoint operators satisfying commutation relations

Model representations are constructed for a system {Bk}1n of bounded linear selfadjoint operators in a Hilbert space H such that; [Bk,Bs] = i/2 φ*Rk,sφ, σkφBs - σsφBk=Rk,s+φ, σkφφ*σs-σsφφ*σk=2iRk,s-, 1≤k, s≤n; where φ is a linear operator from H into a Hilbert space E and {σk,Rk,s±}1n are some selfadjoint operators in E. A realization of these models in function spaces on a Riemann surface is found and a full set of invariants for {Bk}1n is described. Bibliography: 11 titles.