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Mathematics > Representation Theory
Title: Unbounded $\mathfrak{sl}_3$-laminations around punctures
(Submitted on 28 Apr 2024 (v1), last revised 7 May 2024 (this version, v2))
Abstract: 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.
Submission history
From: Tsukasa Ishibashi [view email][v1] Sun, 28 Apr 2024 16:29:31 GMT (79kb)
[v2] Tue, 7 May 2024 05:17:22 GMT (79kb)
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