manuscripta mathematica

, Volume 97, Issue 4, pp 529–543

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

  • A. S. Rapinchuk

DOI: 10.1007/s002290050119

Cite this article as:
Rapinchuk, A. manuscripta math. (1998) 97: 529. doi:10.1007/s002290050119


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.

Mathematics Subject Classification (1991):20C99, 14M99 

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • A. S. Rapinchuk
    • 1
  1. 1.Department of Mathematics, University of Virginia, Kerchof Hall, Charlottesville, VA 22903-3199, USA. e-mail: asr3x@weyl.math.virginia.eduUS

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