  We derive non-linear commutator HS symmetry algebra, which encode unitary
irreducible representations of AdS group subject to Young tableaux
$Y(s_1,...,s_k)$ with $k\geq 2$ rows on $d$-dimensional anti-de-Sitter space.
Auxiliary representations for specially deformed non-linear HS symmetry algebra
in terms of generalized Verma module in order to additively convert a subsystem
of second-class constraints in the HS symmetry algebra into one with
first-class constraints are found explicitly for the case of HS fields for
$k=2$ Young tableaux. The oscillator realization over Heisenberg algebra for
obtained Verma module is constructed. The results generalize the method of
auxiliary representations construction for symplectic $sp(2k)$ algebra used for
mixed-symmetry HS fields on a flat spaces and can be extended on a case of
arbitrary HS fields in AdS-space. Gauge-invariant unconstrained reducible
Lagrangian formulation for free bosonic HS fields with generalized spin
$(s_1,s_2)$ is derived.
