Report
Unbounded $\mathfrak{sl}_3$-laminations around punctures
| العنوان: | Unbounded $\mathfrak{sl}_3$-laminations around punctures |
|---|---|
| المؤلفون: | Ishibashi, Tsukasa, Kano, Shunsuke |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Representation Theory, Mathematics - Geometric Topology, Mathematics - Quantum Algebra |
| الوصف: | We continue to study the unbounded $\mathfrak{sl}_3$-laminations [IK22], with a focus on their structures at punctures. A key ingredient is their relation to the root data of $\mathfrak{sl}_3$. After giving a classification of signed $\mathfrak{sl}_3$-webs around a puncture, we describe the tropicalization of the Goncharov--Shen's Weyl group action in detail. We also clarify the relationship with several other approaches by Shen--Sun--Weng [SSW23] and Fraser--Pylyavskyy [FP21]. Finally, we discuss a formulation of unbounded $\mathfrak{g}$-laminations for a general semisimple Lie algebra $\mathfrak{g}$ in brief. Comment: 57 pages, 26 figures. v2: added a comment on the Roger--Yang relations in p.42. arXiv admin note: text overlap with arXiv:2204.08947 |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2404.18236 |
| رقم الانضمام: | edsarx.2404.18236 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |