  For the quantum walled Brauer algebra, we construct its Specht modules and
(for generic parameters of the algebra) seminormal modules. The latter
construction yields the spectrum of a commuting family of Jucys--Murphy
elements. We also propose a Baxterization prescription; it involves
representing the quantum walled Brauer algebra in terms of morphisms in a
braided monoidal category and introducing parameters into these morphisms,
which allows constructing a "universal transfer matrix" that generates
commuting elements of the algebra.
