A Wakimoto type realization of toroidal $\mathfrak{sl}_{n+1}$

TL;DR

This paper presents a Wakimoto type realization of toroidal rak{sl}_{n+1} using non-commuting differential operators on tensor products of polynomial rings, advancing the understanding of algebraic representations.

Contribution

It introduces a novel Wakimoto type realization for toroidal rak{sl}_{n+1} employing non-commuting differential operators, expanding the representation theory of these algebras.

Findings

Constructed a new realization of toroidal rak{sl}_{n+1}

Utilized non-commuting differential operators in the representation

Representation acts on tensor products of polynomial rings

Abstract

The authors construct a Wakimoto type realization of toroidal $\mathfrak{sl}_{n+1}$ The representation constructed in this paper utilizes non-commuting differential operators acting on the tensor product of two polynomial rings in many commuting variables.