  We propose two new sources of a substantial tensor polarization of sea
partons in the deuteron: the diffractive nuclear shadowing which depends on the
alignment of nucleons in the polarized deuteron and the nuclear excess of pions
in the deuteron which is sensitive to the spin state of the deuteron. The
corresponding tensor structure function $b_{2}(x,Q^{2})$ rises towards small x
and we predict an about one per cent tensor asymmetry
$A_{2}(x,Q^{2})=b_{2}(x,Q^{2})/ F_{2d}(x,Q^{2})$ which by almost two orders in
magnitude exceeds the effect evaluated earlier in the impulse approximation.
The both mechanisms for tensor structure function break the sum rule $\int dx
b_{1}(x,Q^{2})=0$ suggested by Close and Kumano. We comment on the impact of
tensor polarization on the determination of the vector spin structure function
$g_{1d}(x,Q^{2})$ for the deuteron.
