Harmonic superspaces of extended supersymmetry. I. The calculus of harmonic variables

The main technical apparatus of the harmonic superspace approach to extended SUSY, the calculus of harmonic variables on homogeneous spaces of the SUSY automorphism groups is presented in detail for N=2, 3, 4. The authors construct the basic harmonics for the coset manifolds G/H with G=SU(2), H=U(1); G=SU(3), H=SU(2)*H(1) and H=U(1)*U(1); G=SU(4), H=SU(3)*U(1), H=SU(2)*SU(2)*U(1), H=SU(2)*U(1)*U(1) and H=U(1)*U(1), G=USp(2), H=SU(2)*SU(2), H=SU(2)*U(1) and H=U(1)*U(1) and tabulate a number of useful relations between them.