Quantum loop groups and shuffle algebras via Lyndon words.(English)Zbl 07807335
This paper studies PBW bases of the untwisted quantum loop group using the combinatorics of loop words. The authors take a triangular decomposition of the quantum loop group and embed the positive part of this decomposition into a loop version of the shuffle algebra. This, in particular, allows for a description of the roots of this positive parts in terms of the so-called standard Lyndon loop words. As an application, it is shown that a certain homomorphism from the positive half of the quantum loop group to the trigonometric degeneration of Feigin-Odesskii’s shuffle algebra, constructed earlier by Enriquez, is an isomorphism.
Reviewer: Volodymyr Mazorchuk (Uppsala)
MSC:
| 17B37 | Quantum groups (quantized enveloping algebras) and related deformations |
| 17B67 | Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras |
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