On the representations of the braid group constructed by C. M. Egea and E. Galina

In this paper, we determine a sufficient condition for the irreducibility of the family of representations of the braid group constructed by C. M. Egea and E. Galina without requiring that the representations are self-adjoint. Then, we construct a new subfamily of multi-parameter representations $$(\psi _m,V_m), $$ ( ψ m , V m ) , $$1\le m< n$$ 1 ≤ m < n , of dimension $$ V_m =\left( {\begin{array}{c}n\\ m\end{array}}\right) $$ V m = n m . Finally, we study the irreducibility of $$(\psi _m,V_m) $$ ( ψ m , V m ) .