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

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