Jae-Hoon Kwon

We introduce a semisimple tensor category <f>$\\mathcal {O}^{\\rm int}_q(m|n)$</f> of modules over a 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 <f>$B_{m+n}$</f>, <f>$C_{m+n}$</f>, <f>$D_{m+n}$</f>, or <f>$B(0,m+n)$</f> from a viewpoint of super duality. We classify the irreducible modules in <f>$\\mat

Generalizing the super duality formalism for finite-dimensional Lie superalgebras of type A B C D , we establish an equivalence between parabolic Bernstein-Gelfand-Gelfand (BGG) categories of a Kac–Moody Lie superalgebra and a Kac–Moody Lie algebra. The characters for a large family of irreducible highest weight modules over a symmetrizable Kac–Moody Lie superalgebra are then given in terms of Kazhdan–Lusztig polynomials for the first time. We formulate a notion of integrable modules over a symm

We introduce the notion of a crystal base of a finite-dimensional q-deformed Kac module over the quantum superalgebra ⁠, and prove its existence and uniqueness. In particular, we obtain the crystal base of a finite-dimensional irreducible -module with typical highest weight. We also show that the crystal base of a q-deformed Kac module is compatible with that of its irreducible quotient V (λ) given by Benkart, Kang and Kashiwara when V (λ) is an irreducible polynomial representation.

Abstract We introduce a new approach to the study of finite-dimensional representations of the quantum group of the affine Lie superalgebra $ \textrm {L}{\mathfrak {g}\mathfrak {l}}_{M|N}=\mathbb {C}[t,t^{-1}]\otimes \mathfrak {g}\mathfrak {l}_{M|N}$ ($M\neq N$). We explain how the representations of the quantum group of $ \textrm {L}{\mathfrak {g}\mathfrak {l}}_{M|N}$ are directly related to those of the quantum affine algebra of type $A$, using an exact monoidal functor called truncation. This