  The physical and chemical properties of the $\rho$ Ophiuchi A core were
studied using 1.3 mm continuum and molecular lines such as C$^{18}$O,
C$^{17}$O, CH$_3$OH and H$_2$CO observed with the Submillimeter Array (SMA).
The continuum and C$^{18}$O data were combined with the single-dish data
obtained with the IRAM 30m telescope and the James Clerk Maxwell Telescope
(JCMT), respectively. The combined 1.3 mm continuum map reveals three major
sources, SM1, SM1N and VLA1623 embedded in the extended emission running along
the north-south direction, and two additional compact condensations in the
continuum ridge connecting SM1 and VLA1623.The spatial distribution of the
C$^{18}$O emission is significantly different from that of the continuum
emission; the C$^{18}$O emission is enhanced at the eastern and western edges
of the continuum ridge, with its peak brightness temperature of 40--50 K. This
supports the picture that the $\rho$-Oph A core is heated externally from the
nearby stars Oph S1 and HD147889. In contrast, the C$^{18}$O intensity is lower
than 15--20 K at the center of the ridge where the continuum emission is
bright. The C$^{18}$O abundance decreases inside the ridge, and shows
anti-correlation with the N$_2$H$^+$ abundance. However, both C$^{18}$O and
N$_2$H$^+$ show strong depletion at the Class 0 protostar VLA1623, implying
that the dense gas surrounding VLA1623 is colder than the freeze-out
temperature of N$_2$. The blue- and red-shifted components of CH$_3$OH and
H$_2$CO lines are seen at SM1, suggesting outflow activity of embedded source
in SM1, although the spatial distributions do not show clear bipolarity.
