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.

24 pages. arXiv admin note: text overlap with arXiv:2210.12721