Two-parameter quantum affine algebra of type G₂⁽¹⁾, Drinfeld realization and vertex representation

In this paper, we define the two-parameter quantum affine algebra for type G₂⁽¹⁾ and give the (r, s)-Drinfeld realization of G_r, _s (G₂⁽¹⁾) , as well as establish and prove its Drinfeld isomorphism. We construct and verify explicitly the level-one vertex representation of two-parameter quantum affine algebra G_r, _s (G₂⁽¹⁾), which also supports an evidence in nontwisted type G₂⁽¹⁾) for the uniform defining approach via the two-parameter Τ-invariant generating functions proposed in Hu and Zhang [Generating functions with Τ-invariance and vertex representations of two-parameter quantum affine algebras U _r, _s (ĝ): Simply laced cases e-print arXiv:1401.4925].