Super Duality for Quantum Affine Algebras of Type A

Abstract

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 can be viewed as an affine analogue of super duality of type $A$.