Two-parameter Quantum Affine Algebra U_r,s([^(mathfrak sl_n)])U_{r,s}(widehat{mathfrak {sl}_n}), Drinfel’d Realization and Quantum Affine Lyndon Basis

摘要

We further define two-parameter quantum affine algebra U_r,s([^(mathfrak sl_n)])U_{r,s}(widehat{mathfrak {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 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(mathfraksl_n)U_{r,s}({mathfrak{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 affine Lyndon basis we present (with an explicit valid algorithm based on the use of Drinfel’d generators).