Faithful representations of Chevalley groups over quotient rings of non-Archimedean local fields
Mohammad Bardestani
University of Ottawa, CanadaCamelia Karimianpour
University of Ottawa, CanadaKeivan Mallahi-Karai
Jacobs-Universität Bremen, GermanyHadi Salmasian
University of Ottawa, Canada
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Abstract
Let be a non-Archimedean local field with the ring of integers and the prime ideal and let be the adjoint Chevalley group. Let denote the smallest possible dimension of a faithful representation of . Using the Stone–von Neumann theorem, we determine a lower bound for which is asymptotically the same as the results of Landazuri, Seitz and Zalesskii for split Chevalley groups over . Our result yields a conceptual explanation of the exponents that appear in the aforementioned results.
Cite this article
Mohammad Bardestani, Camelia Karimianpour, Keivan Mallahi-Karai, Hadi Salmasian, Faithful representations of Chevalley groups over quotient rings of non-Archimedean local fields. Groups Geom. Dyn. 11 (2017), no. 1, pp. 57–74
DOI 10.4171/GGD/387