  We make a systematic calculation for polarized vector meson production in
semi-inclusive lepton-nucleon deep inelastic scattering $e^-N\to e^-VX$. We
consider the general case of neutral current electroweak interactions at high
energies which give rise to parity-violating effects. We present a general
kinematic analysis for the process and show that the cross sections are
expressed by 81 structure functions. We further give a parton model calculation
for the process and show the results for the structure functions in terms of
the transverse momentum dependent parton distribution functions and
fragmentation functions at the leading order and leading twist of perturbative
quantum chromodynamics. The results show that there are 27 nonzero structure
functions at this order, among which 15 are related to the tensor polarization
of the vector meson. Thirteen structure functions are generated by
parity-violating effects. We also present the result and a rough numerical
estimate for the spin alignment of the vector meson.
