Quantum loop groups and shuffle algebras via Lyndon words

被引：4

作者：

Negut, Andrei ^{[1
,2
]}

Tsymbaliuk, Alexander ^{[3
]}

机构：

[1] MIT, Dept Math, Cambridge, MA 02139 USA

[2] Simion Stoilow Inst Math, Bucharest, Romania

[3] Purdue Univ, Dept Math, W Lafayette, IN USA

来源：

ADVANCES IN MATHEMATICS | 2024年 / 439卷

基金：

美国国家科学基金会;

关键词：

Quantum loop group; Shuffle algebra; Lyndon word; Convex order; Wheel condition; UNIVERSAL R-MATRIX; DRINFELD REALIZATION; CONVEX ORDERINGS; WEYL GROUP; PBW; BASES;

D O I：

10.1016/j.aim.2023.109482

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study PBW bases of the untwisted quantum loop group Uq(Lg) (in the Drinfeld new presentation) using the combinatorics of loop words, by generalizing the treatment of [26,27,39] in the finite type case. As an application, we prove that Enriquez' homomorphism [9] from the positive half of the quantum loop group to the trigonometric degeneration of Feigin-Odesskii's shuffle algebra [13] associated to g is an isomorphism. (c) 2024 Elsevier Inc. All rights reserved.

引用

页数：69

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