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Transformation Groups

, Volume 24, Issue 4, pp 1241–1259 | Cite as

ON ABSTRACT HOMOMORPHISMS OF CHEVALLEY GROUPS OVER THE COORDINATE RINGS OF AFFINE CURVES

  • IGOR A. RAPINCHUKEmail author
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Abstract

The goal of this paper is to establish a general rigidity statement for abstract representations of elementary subgroups of Chevalley groups of rank ≥ 2 over a class of commutative rings that includes the localizations of 1-generated rings and the coordinate rings of affine curves. Our main result implies, for example, that any finite-dimensional representation of SLn(ℤ[X]) (n ≥ 3) over an algebraically closed field of characteristic zero has a standard description, yielding thereby the first unconditional rigidity statement for finitely generated linear groups other than arithmetic groups/lattices.

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsMichigan State UniversityEast LansingUSA

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