  We report a study of the low-mass Class-0 multiple system VLA 1623AB in the
Ophiuchus star-forming region, using H$^{13}$CO$^+$ ($J=3-2$), CS ($J=5-4$),
and CCH ($N=3-2$) lines as part of the ALMA Large Program FAUST. The analysis
of the velocity fields revealed the rotation motion in the envelope and the
velocity gradients in the outflows (about 2000 au down to 50 au). We further
investigated the rotation of the circum-binary VLA 1623A disk as well as the
VLA 1623B disk. We found that the minor axis of the circum-binary disk of VLA
1623A is misaligned by about 12 degrees with respect to the large-scale outflow
and the rotation axis of the envelope. In contrast, the minor axis of the
circum-binary disk is parallel to the large-scale magnetic field according to
previous dust polarization observations, suggesting that the misalignment may
be caused by the different directions of the envelope rotation and the magnetic
field. If the velocity gradient of the outflow is caused by rotation, the
outflow has a constant angular momentum and the launching radius is estimated
to be $5-16$ au, although it cannot be ruled out that the velocity gradient is
driven by entrainments of the two high-velocity outflows. Furthermore, we
detected for the first time a velocity gradient associated with rotation toward
the VLA 16293B disk. The velocity gradient is opposite to the one from the
large-scale envelope, outflow, and circum-binary disk. The origin of its
opposite gradient is also discussed.
