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Abstract Valerij G. Bardakov and P. Bellingeri introduced a new linear representation F ρ ¯ F of degree n+1 n + 1 of the braid group Bₙ B n. We study the irreducibility of this representation. We prove that 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 F ϕ ¯ F.
Mohamad N. Nasser (Wed,) studied this question.
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