%0 Journal Article
%T Two-parameter Quantum Affine Algebra $U_{r,s}(\widehat{\frak {sl}_n})$, Drinfel'd Realization and Quantum Affine Lyndon Basis
%A Naihong Hu
%A Marc Rosso
%A Honglian Zhang
%J Mathematics
%D 2008
%I arXiv
%R 10.1007/s00220-007-0405-1
%X 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).
%U http://arxiv.org/abs/0812.3107v1