Screenings and Vertex Operators of Quantum Superalgebra $U_q(\hat{{sl}}(N|1))$

TL;DR

This paper constructs screening currents and bosonized vertex operators for the quantum superalgebra U_q(\hat{sl}(N|1)), demonstrating their properties and intertwiners for ranks up to 4.

Contribution

It introduces explicit screening currents and bosonizations of vertex operators for U_q(\hat{sl}(N|1)) at arbitrary level, extending previous constructions.

Findings

Screening currents commute with the superalgebra modulo total difference.

Bosonized vertex operators act as intertwiners between Fock-Wakimoto and typical representations.

Results verified for ranks N ≤ 4.

Abstract

We construct the screening currents of the quantum superalgebra $U_q(\hat{sl}(N|1))$ for an arbitrary level $k \neq -N+1$. We show that these screening currents commute with the superalgebra modulo total difference. We propose bosonizations of the vertex operators by using the screening currents. We check that these vertex operators are the intertwiners among the Fock-Wakimoto representation and the typical representation for rank $N \leq 4$.