Geodesic
Super duality and crystal bases for quantum ortho-symplectic superalgebras. II
Journal of Algebraic Combinatorics, Tome 43 (2016) no. 3, pp. 553-588.

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Let $\mathcal{O}^{\mathrm{int}}_q(m\vert n)$ be a semisimple tensor category of modules over a quantum ortho-symplectic superalgebra of type $B$, $C$, $D$ introduced in Part I [Int. Math. Res. Not. 2015, No. 23, 12620--12677 (2015; Zbl 1356.17014)]. 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 $\mathcal {O}^{\mathrm{int}}_q(m\vert n)$ 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 $\mathcal {O}^{\mathrm{int}}_q(m\vert n)$.
Classification : 17B37, 05E10, 17B10
Keywords: quantum group, crystal base, Lie superalgebra, ortho-symplectic Lie superalgebra, tableau 
@article{JAC_2016__43_3_a6,
     author = {Kwon, Jae-Hoon},
     title = {Super duality and crystal bases for quantum ortho-symplectic superalgebras. {II}},
     journal = {Journal of Algebraic Combinatorics},
     pages = {553--588},
     publisher = {mathdoc},
     volume = {43},
     number = {3},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_2016__43_3_a6/}
}
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Kwon, Jae-Hoon. Super duality and crystal bases for quantum ortho-symplectic superalgebras. II. Journal of Algebraic Combinatorics, Tome 43 (2016) no. 3, pp. 553-588. http://geodesic.mathdoc.fr/item/JAC_2016__43_3_a6/