On SS-rigid groups and A. Weil's criterion for local rigidity. I
- Cite this article as:
- Rapinchuk, A. manuscripta math. (1998) 97: 529. doi:10.1007/s002290050119
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We establish some conditions for an abstract finitely generated group Γ to be SS-rigid, i.e. to have only finitely many inequivalent completely reducible representations in each dimension. One of the conditions requires that \(\) be of bounded dimension for all irreducible representatons ρ of Γ, which is reminiscent of A. Weil's criterion for local rigidity. We also link these new conditions to the previous results on the SS-rigidity of groups with bounded generation and verify them for the groups \(\), n≥ 3, and \(\) by purely combinatorial computations.