  We report high resolution 12CO(J = 2-1), 13CO(J = 2-1), and 12CO(J = 3-2)
imaging of the Seyfert 1/starburst ring galaxy NGC 1097 with the Submillimeter
Array to study the physical and kinematic properties of the 1-kpc circumnuclear
starburst ring. Individual star clusters as detected in the HST map of Pa_alpha
line emission have been used to determine the star formation rate, and are
compared with the properties of the molecular gas. The molecular ring has been
resolved into individual clumps at GMA-scale of 200--300 pc in all three CO
lines. The intersection between the dust lanes and the starburst ring, which is
associated with orbit-crowding region, is resolved into two
physically/kinematically distinct features in the 1.5x1.0 (105x70 pc) 12CO(J =
2-1) map. The clumps associated with the dust lanes have broader line width,
higher surface gas density, and lower star formation rate, while the narrow
line clumps associated with the starburst ring have opposite characteristics.
Toomre-Q value under unity at the radius of the ring suggests that the
molecular ring is gravitationally unstable to fragment at the scale of the GMA.
The line widths and surface density of gas mass of the clumps show an azimuthal
variation related to the large scale dynamics. The star formation rate, on the
other hand, is not significantly affected by the dynamics, but has a
correlation with the intensity ratio of 12CO (J = 3-2) and 12CO(J = 2-1), which
traces the denser gas associated with star formation. Our resolved CO map,
especially in the orbit-crowding region, for the first time demonstrates
observationally that the physical/kinematic properties of the GMAs are affected
by the large scale bar-potential dynamics in NGC 1097.
