Reducible higher-spin multiplets in flat and AdS spaces and their geometric frame-like formulation

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We consider the frame-like formulation of reducible sets of totally symmetric bosonic and fermionic higher-spin fields in flat and AdS backgrounds of any dimension, that correspond to so-called higher-spin triplets resulting from the string-inspired BRST approach. The explicit relationship of the fields of higher-spin triplets to the higher-spin vielbeins and connections is found. The gauge invariant actions are constructed including, in particular, the reducible (i.e. triplet) higher-spin fermion case in AdS_D space.
1+49 pages, This is an essentially extended version of the contribution to the volume dedicated to the 60th birthday anniversary of Joseph Buchbinder; v2 FIAN Preprint No and references added

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