The pro-nilpotent Lawrence-Krammer-Bigelow representation

Martin Palmer; Arthur Soulié

doi:10.1016/j.jpaa.2025.107952

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arXiv · 2211.01855

The pro-nilpotent Lawrence-Krammer-Bigelow representation

Martin Palmer·Arthur Soulié

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Abstract

We construct a 3-variable enrichment of the Lawrence-Krammer-Bigelow (LKB) representation of the braid groups, which is the limit of a pro-nilpotent tower of representations having the original LKB representation as its bottom layer. We also construct analogous pro-nilpotent towers of representations of surface braid groups and loop braid groups.

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Martin Palmer, Arthur Soulié. 2022-11-03. The pro-nilpotent Lawrence-Krammer-Bigelow representation. https://doi.org/10.1016/j.jpaa.2025.107952

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