Quantum loop groups and shuffle algebras via Lyndon words
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866929275130609664 |
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| author | Neguţ, Andrei Tsymbaliuk, Alexander |
| author_facet | Neguţ, Andrei Tsymbaliuk, Alexander |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2102_11269 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Quantum loop groups and shuffle algebras via Lyndon words Neguţ, Andrei Tsymbaliuk, Alexander Representation Theory Combinatorics Quantum Algebra 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. |
| title | Quantum loop groups and shuffle algebras via Lyndon words |
| topic | Representation Theory Combinatorics Quantum Algebra |
| url | https://arxiv.org/abs/2102.11269 |