, Volume 97, Issue 4, pp 529-543

On SS-rigid groups and A. Weil's criterion for local rigidity. I

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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.

Received: 17 April 1998 / Revised version: 30 June 1998