Inelastic J/psi production at HERA in the colour singlet model with k_T-factorization

In the framework of k_T-factorization QCD approach and the colour singlet model we consider J/\psi inelastic photo- and leptoproduction processes at HERA. We investigate the dependences of the single differential and double differential cross section on different forms of the unintegrated gluon distribution. The z and p_T dependences of the spin aligment parameter \alpha are presented also. Our theoretical predictions agree well with recent data taken by the H1 and ZEUS collaborations at HERA. It is shown that experimental study of the polarization J/\psi mesons at low Q^2 < 1 GeV^2 is an additional test of BFKL gluon dynamics.