Super duality and crystal bases for quantum ortho-symplectic superalgebras II

Let \(\mathcal {O}^\mathrm{int}_q(m|n)\) be a semisimple tensor category of modules over a quantum ortho-symplectic superalgebra of type B, C, D introduced in Kwon (Int Math Res Not, 2015. doi: 10.1093/imrn/rnv076). It is a natural counterpart of the category of finitely 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 (Kwon in Int Math Res Not, 2015. doi: 10.1093/imrn/rnv076), we classify the irreducible modules in \(\mathcal {O}^\mathrm{int}_q(m|n)\) and prove 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 analog gives a realization of crystals for the highest weight modules in \(\mathcal {O}^\mathrm{int}_q(m|n)\).