Super duality and Crystal bases for quantum orthosymplectic superalgebras II

الأصل · EN

Let Ointq(m|n) be a semisimple tensor category of modules over a quantum ortho-symplectic superalgebra of type B, C, D introduced in the author's previous work. 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, we classify the irreducible modules in Ointq(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 analogue gives a realization of crystals for the highest weight modules in Ointq(m|n).