Necessary and sufficient conditions for the irreducibility of a linear representation of the braid group $$B_n$$ B n

Abstract

Abstract Valerij G. Bardakov and P. Bellingeri introduced a new linear representation $$\bar{\rho }_F$$ ρ ¯ F of degree $$n+1$$ n + 1 of the braid group $$B_n$$ B n . We study the irreducibility of this representation. We prove that $$\bar{\rho }_F$$ ρ ¯ F is reducible to the degree $$n-1$$ n - 1 . Moreover, we give necessary and sufficient conditions for the irreducibility of the complex specialization of its $$n-1$$ n - 1 degree composition factor $$\bar{\phi }_F$$ ϕ ¯ F .

Keywords

• 20F36