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Let $\mathcal{O}^{int}_q(m|n)$ be a semisimple tensor category of modulesover a quantum ortho-symplectic superalgebra of type $B, C, D$ introduced inthe author's previous work. It is a natural counterpart of the category offinitely dominated integrable modules over a quantum group of type $B, C, D$from a viewpoint of super duality. Continuing the previous work on type $B$ and$C$, we classify the irreducible modules in $\mathcal{O}^{int}_q(m|n)$, andprove the existence and uniqueness of their crystal bases in case of type $D$.A new combinatorial model of classical crystals of type $D$ is introduced,whose super analogue gives a realization of crystals for the highest weightmodules in $\mathcal{O}^{int}_q(m|n)$.

Super duality and Crystal bases for quantum orthosymplectic superalgebras II