A note on $SU(1,1\mathrm{\mid }n)$ and $OSp(6\mathrm{\mid }2)$ superconformal mechanics

In this article we consider the construction of the superconformal mechanics that realize $SU(1,1\mathrm{\mid }n)$ and $OSp(6\mathrm{\mid }2)$ symmetries and involve interactions with non-Abelian bosonic currents. If is shown that for $N>4$ supersymmetries the currents involved have to satisfy the algebraic equations. General considerations on methods of solving these equations are given. In the obtained particular solutions currents are expressed in terms of semi-dynamical variables (harmonics), and, on one instance, coordinates and momenta.