Generating Functions with $\tau$-Invariance and Vertex Representations of Quantum Affine Algebras $U_{r,s}(\hat{\mathfrak{g}})$ (I): Simply-laced Cases

Abstract

We put forward the exact version of two-parameter generating functions with $\tau$-invariance, which allows us to give a unified and inherent definition for the Drinfeld realization of two-parameter quantum affine algebras for all the untwisted types. As verification, we first construct their level-one vertex representations of $U_{r,s}(\hat{\mathfrak{g}})$ for simply-laced types, which in turn well-detect the effectiveness of our definitions both for $(r,s)$-generating functions and $(r,s)$-Drinfeld realization in the framework of establishing the two-parameter vertex representation theory.

44 pages

Cited by in corpus (2)

• Two-parameter twisted quantum affine algebras
• Two-parameter Quantum Affine Algebra of Type ${\mathrm{C}}_n^{(1)},$ Drinfeld Realization and Vertex Representation