Quantum loop groups and shuffle algebras via Lyndon words

Abstract

We study PBW bases of the untwisted quantum loop group $U_q(L\mathfrak{g})$ (in the Drinfeld new presentation) using the combinatorics of loop words, by generalizing the treatment of [29,30,43] in the finite type case. As an application, we prove that Enriquez' homomorphism [11] from the positive half of the quantum loop group to the trigonometric degeneration of Feigin-Odesskii's elliptic algebra [15] associated to $\mathfrak{g}$ is an isomorphism.

References in corpus (2)

• Two-parameter Quantum Affine Algebra $U_{r,s}(\widehat{{\mathfrak{sl}}_n})$, Drinfel'd Realization and Quantum Affine Lyndon Basis
• Shuffle algebra realizations of type $A$ super Yangians and quantum affine superalgebras for all Cartan data

Cited by in corpus (5)

• Shuffle algebras and their integral forms: specialization map approach in types $B_n$ and $G_2$
• Fusion and specialization for type ADE shuffle algebras
• Affine Standard Lyndon words: A-type
• Shuffle algebras and their integral forms: specialization map approach in types $C_n$ and $D_n$
• Standard Lyndon loop words: weighted orders