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arXiv · 2201.07153

Braid groups and symplectic Steinberg groups

François Digne·Christian Kassel
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Abstract

We construct a homomorphism $f$ from the braid group $B_{2n+2}$ on $2n+2$ strands to the Steinberg group associated with the Lie type $C_n$ and with integer coefficients. This homomorphism lifts the well-known symplectic representation of the braid groups. We also describe the image and the kernel of $f$.

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François Digne, Christian Kassel. 2022-01-18. Braid groups and symplectic Steinberg groups. https://doi.org/10.2140/akt.2023.8.669

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