Oscillator representations of quantum affine orthosymplectic superalgebras II

As a continuation of our study on quantum affine spin-oscillator correspondence, we introduce a category of $q$-oscillator representations of quantum affine superalgebras of type $XB$ ($X=B,D$) and construct irreducible objects in a uniform way. Under the truncation functor inspired by the theory of super duality, they are related to finite-dimensional irreducible representations of $U_q(D_{n+1}^{(2)})$ ($X=B$) or $U_q(B_n^{(1)})$ ($X=D$). We also considerably streamline our previous arguments, which clarifies how our construction can be understood as a quantum affinization of classical super duality.