Bosonization and vertex operator of supersymmetry $u_q(\hat{sl}(n|1))$ for level $k$

TL;DR

This paper develops a bosonization framework for the quantum superalgebra $U_q(\\hat{sl}(N|1))$ at any level, including construction of screening operators and vertex operators for representation theory applications.

Contribution

It introduces a novel bosonization method for $U_q(\hat{sl}(N|1))$ at arbitrary levels, along with explicit screening and vertex operator constructions.

Findings

Bosonization valid for all levels $k$

Explicit screening operators constructed

Vertex operators for intertwiners proposed

Abstract

We construct a bosonization of the quantum superalgebra $U_q(\hat{sl}(N|1))$ for an arbitrary level $k$. We construct the screening that commutes with the quantum superalgebra for an arbitrary level $k \neq -N+1$. We propose a bosonization of the vertex operator that gives the intertwiner among the Wakimoto realization and the typical representation.