Length-two representations of quantum affine superalgebras and Baxter operators

TL;DR

This paper explores the structure of quantum affine superalgebras, defining Baxter operators via transfer matrices and deriving Bethe Ansatz Equations, advancing understanding of quantum integrable models.

Contribution

It introduces new short exact sequences of representations for quantum affine superalgebras and constructs Baxter operators from these representations.

Findings

Defined Baxter operators as transfer matrices.

Derived Bethe Ansatz Equations.

Established relations involving infinite-dimensional representations.

Abstract

Associated to quantum affine general linear Lie superalgebras are two families of short exact sequences of representations whose first and third terms are irreducible: the Baxter TQ relations involving infinite-dimensional representations; the extended T-systems of Kirillov--Reshetikhin modules. We make use of these representations over the full quantum affine superalgebra to define Baxter operators as transfer matrices for the quantum integrable model and to deduce Bethe Ansatz Equations, under genericity conditions.