In this paper, we calculate decomposition matrices of the Birman-Murakami-Wenzl algebras over $mathbb C$.
In this paper, we establish explicit relationship between decomposition numbers of quantized walled Brauer algebras and those for either Hecke algebras associated to certain symmetric groups or (rational) $q$-Schur algebras over a field $kappa$. This
enables us to use Arikis result cite{Ar} and Varagnolo-Vasserots result cite{VV} to compute such decomposition numbers via inverse Kazhdan-Lusztig polynomials associated with affine Weyl groups of type $A$ if the ground field is $mathbb C$.
In this paper, we give a criterion on the semisimplicity of quantized walled Brauer algebras $mathscr B_{r,s}$ and classify its simple modules over an arbitrary field $kappa$.
