Super duality for quantum affine algebras of type $A$

TL;DR

This paper introduces a new approach linking finite-dimensional representations of quantum affine superalgebras to those of quantum affine algebras of type A through a truncation functor, extending super duality to the affine case.

Contribution

It establishes a direct connection between representations of quantum affine superalgebras and quantum affine algebras of type A via an exact monoidal functor, providing an affine super duality framework.

Findings

Established a truncation functor relating superalgebra and algebra representations.

Demonstrated the affine analogue of super duality of type A.

Provided a new perspective on finite-dimensional representations of quantum affine superalgebras.

Abstract

We introduce a new approach to the study of finite-dimensional representations of the quantum group of the affine Lie superalgebra $\mathrm{L}\mathfrak{gl}_{M|N}=\mathbb{C}[t,t^{-1}]\otimes\mathfrak{gl}_{M|N}$ ($M\neq N$). We explain how the representations of the quantum group of $\mathrm{L}\mathfrak{gl}_{M|N}$ 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 $A$.