  We previously observed the star-forming region G16.59$-$0.05 through
interferometric observations of both thermal and maser lines, and identified a
high-mass young stellar object (YSO) which is surrounded by an accretion disk
and drives a nonthermal radio jet. We performed high-angular-resolution (beam
FWHM ~0.15") 1.2-mm continuum and line observations towards G16.59$-$0.05 with
the Atacama Large Millimeter Array (ALMA). The main dust clump, with size
~10$^4$ au, is resolved into four relatively compact (diameter ~2000 au)
millimeter (mm) sources. The source harboring the high-mass YSO is the most
prominent in molecular emission. By fitting the emission profiles of several
unblended and optically thin transitions of CH$_3$OCH$_3$ and CH$_3$OH, we
derived gas temperatures inside the mm-sources in the range 42--131 K, and
calculated masses of 1--5 $M_{\odot}$. A well-defined Local Standard of Rest
velocity (Vlsr) gradient is detected in most of the high-density molecular
tracers at the position of the high-mass YSO, pinpointed by compact 22-GHz
free-free emission. This gradient is oriented along a direction forming a large
(~70 degree) angle with the radio jet, traced by elongated 13-GHz continuum
emission. The butterfly-like shapes of the P-V plots and the linear pattern of
the emission peaks of the molecular lines at high velocity confirm that this
Vlsr gradient is due to rotation of the gas in the disk surrounding the
high-mass YSO. The disk radius is ~500 au, and the Vlsr distribution along the
major axis of the disk is well reproduced by a Keplerian profile around a
central mass of 10$\pm$2 $M_{\odot}$. The position of the YSO is offset by >~
0.1" from the axis of the radio jet and the dust emission peak. To explain this
displacement we argue that the high-mass YSO could have moved from the center
of the parental mm source owing to dynamical interaction with one or more
companions.
