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

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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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Authors and Affiliations

  1. Department of Mathematics, Michigan State University, East Lansing, MI, 48824, USA

    IGOR A. RAPINCHUK

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  1. IGOR A. RAPINCHUK
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Correspondence to IGOR A. RAPINCHUK.

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To Gregory A. Margulis on his 70th birthday

Partially supported by an AMS-Simons Travel Grant.

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RAPINCHUK, I.A. ON ABSTRACT HOMOMORPHISMS OF CHEVALLEY GROUPS OVER THE COORDINATE RINGS OF AFFINE CURVES. Transformation Groups 24, 1241–1259 (2019). https://doi.org/10.1007/s00031-018-9494-5

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  • DOI: https://doi.org/10.1007/s00031-018-9494-5

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