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arXiv · 2412.12802

Presentations of the braid group of the complex reflection group $G(d,d,n)$

Francesca Fedele·Bethany Rose Marsh
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Abstract

We show that the braid group associated to the complex reflection group $G(d,d,n)$ is an index $d$ subgroup of the braid group of the orbifold quotient of the complex numbers by a cyclic group of order $d$. We also give a compatible presentation of $G(d,d,n)$ and its braid group for each tagged triangulation of the disk with $n$ marked points on its boundary and an interior marked point (interpreted as a cone point of degree $d$) in such a way that the presentations of Brou\'{e}-Malle-Rouquier correspond to a special tagged triangulation.

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BibTeXRIS

Francesca Fedele, Bethany Rose Marsh. 2024-12-17. Presentations of the braid group of the complex reflection group $G(d,d,n)$. https://arxiv.org/abs/2412.12802

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