The instabilities of the sidewall boundary layer in a rapidly rotating split cylinder are studied numerically. Axisymmetric results are studied extensively where a variety of different states are found. In the basic state, the interior flow is in solid-body rotation with the mean rotation rate of the two cylinder halves. The sidewall boundary layer of the basic state is compared with theoretical results. For sufficiently fast mean rotation and large enough differential rotation between the two halves, instabilities in the boundary layer appear. These instabilities result in periodic and quasi-periodic states in different parameter regimes. The instabilities are localized in the boundary layer, but they may transport shear into interior if their associated frequencies are less than twice the mean rotation frequency, and then only in the form of inertial wave beams along directions determined by the frequencies.