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

Abstract

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 $$\mathcal {O}^\mathrm{int}_q(m|n)$$ .