Two-parameter Quantum Affine Algebra of Type ${\mathrm C_n^{(1)}},$ Drinfeld Realization and Vertex Representation

TL;DR

This paper constructs a level-one quantum vertex operator representation for the two-parameter quantum affine algebra of type C_n^{(1)}, generalizing previous one-parameter models and providing explicit Drinfeld realization.

Contribution

It provides an explicit construction of the two-parameter quantum vertex operator representation based on Drinfeld realization for type C_n^{(1)}.

Findings

Explicit two-parameter quantum vertex operator representation constructed.

Degeneration to one-parameter case when rs=1 demonstrated.

Provides a foundation for further studies of two-parameter quantum affine algebras.

Abstract

The two-parameter quantum vertex operator representation of level-one is explicitly constructed for $U_{r,s}(C^{(1)}_n)$ based on its two-parameter Drinfeld realization we give. This construction will degenerate to the one-parameter case due to Jing-Koyama-Misra (\cite{JKM2}) when $rs=1$.