On the realization of infinite (continuous) spin field representations in AdS${}_{\mathbf{4}}$ space

We study the symmetry properties of infinite spin fields in $\rm{AdS}_4$ space which are involved in the Lagrangian model proposed in arXiv:2403.14446 where the main role is played by operator constraints. It is shown that the conditions defining infinite spin states in $\rm{AdS}_4$ space are $\mathrm{SO}(2,3)$-invariant. It is found that in the model under consideration the Casimir operators are completely fixed by the constraint operators and only one of the Casimir operators is independent. It is shown that in this model, infinite spin fields in $\rm{AdS}_4$ space are described by the most degenerate representations of the $\mathrm{SO}(2,3)$ group.