Level $-1/2$ realization of quantum N-toroidal algebras in type $C_n$

TL;DR

This paper constructs a level -1/2 vertex representation for quantum N-toroidal algebras of type C_n, extending the understanding of their structure and representations.

Contribution

It introduces a novel level -1/2 vertex representation for quantum N-toroidal algebras of type C_n, generalizing previous models.

Findings

Provides a new vertex representation at level -1/2

Derives a vertex representation for quantum toroidal algebra of type C_n

Enhances the theoretical framework for quantum N-toroidal algebras

Abstract

We construct a level $-\frac{1}{2}$ vertex representation of the quantum N-toroidal algebra for type $C_n$, which is a natural generalization of the usual quantum toroidal algebra. The construction also provides a vertex representation of the quantum toroidal algebra for type $C_n$ as a by-product.