The multi-virtual twin group M_kVT_n admits exactly eight distinct homogeneous 2-local representations into GL_n(C) for n >= 3; these are generally unfaithful but irreducible under explicit conditions, with induced non-local representations constructed for the pure subgroup.
Nasser,Local extensions andΦ-type extensions of some local represen- tations of the braid groupBn to the singular braid monoidSMn, Vietnam Journal of Mathematics, 1–12, (2025)
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Presentations and Representations of the Multi-Virtual Twin Group and Associated Subgroups
The multi-virtual twin group M_kVT_n admits exactly eight distinct homogeneous 2-local representations into GL_n(C) for n >= 3; these are generally unfaithful but irreducible under explicit conditions, with induced non-local representations constructed for the pure subgroup.