The braid group \(B_4\) is linear (Q5926380)

The author studies a linear representation \(\rho\colon B_n\to\text{GL}_m(\mathbb{Z}[q^{\pm 1},t^{\pm 1}])\) (where \(m=n(n-1)/2\)). Instead of the usual Artin presentation of \(B_n\), the author uses a new presentation with a new generating subset \(Q\) and formulates a relation for the Charney length function with respect to \(Q\). He formulates a conjecture implying that: (a) \(\rho\) is faithful, (b) the Charney length function with respect to \(Q\) satisfies the relation. The author proves this conjecture for \(n=4\).