We further define two-parameter quantum affine algebra $U_{ r,s}(\widehat{ \frak { sl}_n})$ $(n>2)$ after the work on the finite cases (see [BW1], [BGH1], [HS] & [BH]), which turns out to be a Drinfel'd double. Of importance for the quantum { \it affine} cases is that we can work out the compatible two-parameter version of the Drinfel'd realization as a quantum affinization of $U_{ r,s}(\frak{ sl}_n)$ and establish the Drinfel'd isomorphism Theorem in the two-parameter setting, via developing a new combinatorial approach (quantum calculation) to the quantum { \it affine} Lyndon basis we present (with an explicit valid algorithm based on the use of Drinfel'd generators).
Categories: math.QA math.RT