On an approximation property for nondiscrete inequivalent representations of finitely generated groups |
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| Institution: | 1. Neuroscience Center, Department of Neurology, The First Hospital of Jilin University, Changchun, China;2. Department of Neurobiology, Care Sciences & Society, Division of Neurogeriatrcs, Karolinska Institutet, Karolinska University Hospital Solna, Stockholm, Sweden;1. National Centre for Nano Fabrication and Characterization, DTU Nanolab, Technical University of Denmark, Ørsteds Plads, Building 347, 2800 Kgs. Lyngby, Denmark;2. National Food Institute, DTU Food, Technical University of Denmark, Kemitorvet, Building 202, 2800 Kgs. Lyngby, Denmark |
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| Abstract: | Let R(Γ, G) be the variety of representations of a finitely generated group Γ in a simple complex algebraic group G. We establish some sufficient conditions for the image of the diagonal representation ϱ = (ϱ1, …, ϱt), ϱi ε R(Γ, G), to be dense in Gf in the complex topology (“weak approximation”). |
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