  The SU(N) Heisenberg model with various single-row representations is
investigated by quantum Monte Carlo simulations. While the zero-temperature
phase boundary agrees qualitatively with the theoretical predictions based on
the 1/N expansion, some unexpected features are also observed. For N>=5 with
the fundamental representation, for example, it is suggested that the ground
states possess exact or approximate U(1) degeneracy. In addition, for the
representation of Young tableau with more than one column, the ground state
shows no valence-bond-solid order even at N greater than the threshold value.
