Every complex local representation of TVB2 into GL3(C) belongs to one of eight explicit families, and similar families are listed for TVBn into GL_{n+1}(C) and for STVB2 into M3(C).
Birman, Braids, Links and Mapping Class Groups, Annals of Mathematical stud- ies, Princeton University Press, 82 (1974)
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Matrix representations of the twisted virtual braid group and its extensions
Every complex local representation of TVB2 into GL3(C) belongs to one of eight explicit families, and similar families are listed for TVBn into GL_{n+1}(C) and for STVB2 into M3(C).