The $q$-Wakimoto Realization of the Superalgebras $U_q(\hat{sl}(N|1))$ and $U_{q,p}(\hat{{sl}}(N|1))$

TL;DR

This paper presents a bosonization method called the $q$-Wakimoto realization for superalgebras $U_q(\hat{sl}(N|1))$ and $U_{q,p}(\hat{sl}(N|1))$, applicable at any level, expanding the tools for studying quantum affine superalgebras.

Contribution

It introduces a novel $q$-Wakimoto realization for these superalgebras using the $\xi$-$\eta$ system, generalizing previous bosonization techniques.

Findings

Provides explicit bosonizations for arbitrary level $k$.

Defines the $q$-Wakimoto realization via the $\xi$-$\eta$ system.

Enables new approaches to quantum affine superalgebra representations.

Abstract

We give bosonizations of the superalgebras $U_q(\hat{sl}(N|1))$ and $U_{q,p}(\hat{sl}(N|1))$ for an arbitrary level $k \in {\bf C}$. We introduce the submodule by the $\xi$-$\eta$ system, that we call the $q$-Wakimoto realization.