# A Bosonization of $U_q(\widehat{sl}(M|N))$

## TL;DR

This paper develops a bosonization framework for the quantum affine superalgebra $U_q(\\widehat{sl}(M|N))$ at any level, introducing screening operators that commute with the algebra for specific levels.

## Contribution

It provides a new bosonization method for $U_q(\widehat{sl}(M|N))$ applicable at arbitrary levels, including explicit screening operators for levels other than -M+N.

## Key findings

- Bosonization formulas for $U_q(\widehat{sl}(M|N))$ at any level.
- Explicit construction of screening operators for levels $k
eq -M+N$.
- Extension of bosonization techniques to quantum affine superalgebras.

## Abstract

A bosonization of the quantum affine superalgebra $U_q(\widehat{sl}(M|N))$ is presented for an arbitrary level $k \in {\bf C}$. Screening operators that commute with $U_q(\widehat{sl}(M|N))$ are presented for the level $k \neq -M+N$.