On the semisimplicity of the cyclotomic Brauer algebras, II

In this paper, we give a necessary and sufficient condition for the semisimplicity of cyclotomic Brauer algebras Bm,n(δ) of types G(m,1,n) with m⩾2. This generalizes [H. Rui, A criterion on the semisimple Brauer algebras, J. Combin. Theory Ser. A 111 (2005) 78–88, 1.2–1.3] and [H. Rui, M. Si, A criterion on the semisimple Brauer algebras, II, J. Combin. Theory Ser. A 113 (2006) 1199–1203, 2.5] on Brauer algebras.