Abstract
AbstractValerij 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
.
Publisher
Springer Science and Business Media LLC
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