Basic monodromy operator for quantum superalgebra

Abstract

We derive the explicit form of the basic monodromy operator for the quantum loop superalgebra $\mathrm{U}_q(\mathcal{L}(\mathfrak{sl}_{2|1}))$. Two significant additional results emerge from this derivation: simple expressions for the generating functions of the the images of the root vectors of $\mathrm{U}_q(\mathcal{L}(\mathfrak{sl}_{2|1}))$ under the Jimbo homomorphism and explicit expressions for certain central elements of the quantum superalgebra $\mathrm{U}_q(\mathfrak{gl}_{2|1})$. Furthermore, we establish the relationship between these central elements and those obtained by using the Drinfeld partial trace method.