A bstract We present new explicit realizations of the most general N = 4 $$ mathcal{N}=4 $$ , d = 1 superconformal symmetry D (2 , 1; α ) in the models of N = 4 $$ mathcal{N}=4 $$ superconformal mechanics based on the reducible multiplets ( 1 , 4 , 3 ) ⊕ ( 0 , 4 , 4 ), ( 3 , 4 , 1 ) ⊕ ( 0 , 4 , 4 ) and ( 4 , 4 , 0 ) ⊕ ( 0 , 4 , 4 ). We start from the manifestly supersymmetric superfield actions for these systems and then descend to the relevant off- and on-shell component actions from which we derive the D (2 , 1; α ) (super)charges by the Noether procedure. Some peculiarities of these realizations of D (2 , 1; α ) are discussed. We also construct a new D (2 , 1; α ) invariant system by joining the multiplets ( 3 , 4 , 1 ) and ( 4 , 4 , 0 ) in such a way that they interact with each other through an extra ( 0 , 4 , 4 ) multiplet. New fermionic conformal couplings appear as the result of elimination of the appropriate auxiliary fields.
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