Braid groups and symplectic Steinberg groups

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 $f$.

21 pages. The statement and proof of Theorem 5.7 have been corrected in Version 2. Sections 5.4 and 6 were added in Version 3. Remark 5.9 added in Version 4. In Version 5: slight changes in introduction, Section 4 and acknowledgement; two references added

References in corpus (3)

• Generators for the hyperelliptic Torelli group and the kernel of the Burau representation at t=-1
• On an action of the braid group B_{2g+2} on the free group F_{2g}
• A braid-like presentation of the integral Steinberg group of type $C_2$