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In the framework of light-cone gauge approach, bosonic and fermionicmixed-symmetry continuous-spin fields in AdS space and flat space areconsidered. For such fields, the light-cone gauge actions are found.Realization of relativistic symmetries of AdS and flat spaces on thecontinuous-spin fields is also presented. Simple realization of spin operatorsis found. With respect to vector variable entering the continuous-spin fields,the spin operators for the fields in flat space turn out to be first-orderdifferential operators, while, for the the fields in AdS space, the spinoperators are realized as the second-order differential operators. By product,we obtain also the simple description of triplectic mixed-symmetrycontinuous-spin fields.

Mixed-symmetry continuous-spin fields in flat and AdS spaces