Super duality and Crystal bases for quantum orthosymplectic superalgebras II

Abstract

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

37 pages with a minor revision on v1 and v2. Some figures have been added

References in corpus (2)

• Howe duality and Kostant Homology Formula for infinite-dimensional Lie superalgebras
• Irreducible Characters of Kac-Moody Lie superalgebras

Cited by in corpus (8)

• Characterization of queer supercrystals
• Flagged Littlewood-Richardson tableaux and branching rule for classical groups
• On the Harish-Chandra Homomorphism for Quantum Superalgebras
• Combinatorial Howe duality of symplectic type
• Lusztig data of Kashiwara-Nakashima tableaux in type D
• 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
• Extremal weight crystals over affine Lie algebras of infinite rank