Abstract
We study the many-body ground states of SU(N) symmetric hardcore bosons on the topological flat-band model by using controlled numerical calculations. By introducing strong intracomponent and intercomponent interactions, we demonstrate that a hierarchy of bosonic SU(N) fractional quantum Hall (FQH) states emerges at fractional filling factors ν=N/(MN+1) (odd M=3). In order to characterize this series of FQH states, we figure the effective K matrix from the inverse of the Chern number matrix. The topological characterization of the K matrix also reveals quantized drag Hall responses and fractional charge pumping that could be detected in future experiments. In addition, we address the general one-to-one correspondence to the spinless FQH states in topological flat bands with Chern number C=N at fillings ν=1/(MC+1).