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

In the framework of light-cone gauge approach, bosonic and fermionic mixed-symmetry continuous-spin fields in AdS space and flat space are considered. For such fields, the light-cone gauge actions are found. Realization of relativistic symmetries of AdS and flat spaces on the continuous-spin fields is also presented. Simple realization of spin operators is 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-order differential operators, while, for the fields in AdS space, the spin operators are realized as the second-order differential operators. By product, we obtain also the simple description of triplectic mixed-symmetry continuous-spin fields.