BRST construction for infinite spin field on $Ad{S}_4$

We generalize the first class constraints that describe the infinite spin irreducible $4D$ Poincaré group representation in flat space to new first class constraints in $Ad{S}_4$ space. The constraints are realized as operators acting in Fock space spanned by the creation and annihilation operators with two-component spinor indices. As a result, we obtain a new closed gauge algebra on $Ad{S}_4$ with the known flat space limit. Using this gauge algebra, we construct the BRST charge and derive the Lagrangian and gauge transformations for free bosonic infinite spin field theory in $Ad{S}_4$ space.