  We examine the combined effects of Rashba spin-orbit (SO) coupling and
rotation on trapped spinor Bose-Einstein condensates (BECs). Nature of single
particle states is thoroughly examined in the Landau level basis and is shown
to support the formation of half-quantum vortex. In the presence of weak s-wave
interactions, the ground state at strong SO coupling develops ring-like
structures with domains whose number shows step behavior with increasing
rotation. For fast rotation case, the vortex pattern favors triangular lattice,
accompanied by the density depletion in the central region and weakened
Skyrmionic character as the SO coupling is enhanced. Giant vortex formation is
facilitated when SO coupling and rotation are both strong.
