We generalize the first class constraints that describe the infinite spin irreducible $4D$ Poincar\'{e} group representation in flat space to new first class constraints in AdS₄ 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 AdS₄ 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 AdS₄ space.
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Buchbinder et al. (2024) studied this question.
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