Complete classification of complex local representations of FVB_2 into GL_2(C) into 12 types with irreducibility and faithfulness conditions, extended to homogeneous cases for FVB_n into GL_n(C) and GL_{n+1}(C).
Moody,The Burau representation of the braid groupB n is not faithful for largen, Bull
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Local Representations of the Flat Virtual Braid Group
Complete classification of complex local representations of FVB_2 into GL_2(C) into 12 types with irreducibility and faithfulness conditions, extended to homogeneous cases for FVB_n into GL_n(C) and GL_{n+1}(C).