Free massless fermionic fields of arbitrary spins s>0 corresponding to totally (anti)symmetric tensor - spinor representations of the SO(d-1) compact subgroup and in d-dimensional anti-de Sitter space are investigated. We propose the free equations of motion, subsidiary conditions and corresponding gauge transformations for such fields. The equations obtained are used to derive the lowest energy values for the above-mentioned representations. A new representation for equations of motion and gauge transformations in terms of generators of the anti-de Sitter group SO(d-1,2) is found. It is demonstrated that in contrast to the symmetric case the gauge parameter of the antisymmetric massless field is also a massless field.
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