Two-parameter Quantum Affine Algebra $U_{r,s}(\widehat{{\mathfrak{sl}}_n})$, Drinfel'd Realization and Quantum Affine Lyndon Basis

Abstract

We further define two-parameter quantum affine algebra $U_{r,s}(\widehat{{\mathfrak{sl}}_n})$ $(n>2)$ 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 {\it affine} cases is that we can work out the compatible two-parameter version of the Drinfel'd realization as a quantum affinization of $U_{r,s}({\mathfrak{sl}}_n)$ and establish the Drinfel'd isomorphism Theorem in the two-parameter setting, via developing a new combinatorial approach (quantum calculation) to the quantum {\it affine} Lyndon basis we present (with an explicit valid algorithm based on the use of Drinfel'd generators).

31 pages

References in corpus (4)

• Braid Group Action and Quantum Affine Algebras
• Convex Bases of PBW type for Quantum Affine Algebras
• Drinfel'd Doubles and Lusztig's Symmetries of Two-Parameter Quantum Groups
• Drinfeld comultiplication and vertex operators

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