Super duality and Crystal bases for quantum orthosymplectic superalgebras

Abstract

We introduce a semisimple tensor category $\mc{O}^{int}_q(m|n)$ of modules over an quantum ortho-symplectic superalgebra. It is a natural counterpart of the category of finitely dominated integrable modules over the quantum classical (super) algebra of type $B_{m+n}$, $C_{m+n}$, $D_{m+n}$ or $B(0,m+n)$ from a viewpoint of super duality. We classify the irreducible modules in $\mc{O}^{int}_q(m|n)$ and show that an irreducible module in $\mc{O}^{int}_q(m|n)$ has a unique crystal base in case of type $B$ and $C$. An explicit description of the crystal graph is given in terms of a new combinatorial object called ortho-symplectic tableaux.

53 pages, Sections 3 and 4 have been revised

References in corpus (2)

• Super duality and Crystal bases for quantum orthosymplectic superalgebras II
• Howe duality and Kostant Homology Formula for infinite-dimensional Lie superalgebras

Cited by in corpus (10)

• Characterization of queer supercrystals
• Super duality and Crystal bases for quantum orthosymplectic superalgebras II
• Irreducible Characters of Kac-Moody Lie superalgebras
• Flagged Littlewood-Richardson tableaux and branching rule for classical groups
• On the Harish-Chandra Homomorphism for Quantum Superalgebras
• Combinatorial Howe duality of symplectic type
• Crystal base of the negative half of the quantum superalgebra $U_q(\mathfrak{gl}(m|n))$
• Crystal bases of parabolic Verma modules over the quantum orthosymplectic superalgebras
• A categorification of $\mathfrak{q}(2)$-crystals
• Crystal interpretation of a formula on the branching rule of types $B_n$, $C_n$, and $D_n$