Basic monodromy operator for quantum superalgebra

TL;DR

This paper derives the explicit form of the basic monodromy operator for the quantum loop superalgebra U_q(sl_{2|1}) and provides new formulas for root vector images and central elements, linking different construction methods.

Contribution

It presents the explicit basic monodromy operator for U_q(sl_{2|1}), new expressions for root vector images under the Jimbo homomorphism, and relates central elements from different approaches.

Findings

Explicit form of the monodromy operator for U_q(sl_{2|1})

New formulas for root vector images under Jimbo homomorphism

Relations between central elements from different constructions

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.