Free equations for massive matter fields in $2+1$-dimensional anti-de Sitter space from deformed oscillator algebra

We reformulate free equations of motion for massive spin 0 and spin 1/2 matter fields in $2+1$-dimensional anti-de Sitter space in the form of some covariant constancy conditions. The infinite-dimensional representation of the anti-de Sitter algebra underlying this formulation is shown to admit a natural realization in terms of the algebra of deformed oscillators with a deformation parameter related to the parameter of mass.