Geodesic
Faithful representations of Chevalley groups over quotient rings of non-Archimedean local fields
Mohammad Bardestani1 ; Camelia Karimianpour1 ; Keivan Mallahi-Karai2 orcid ; Hadi Salmasian1
1University of Ottawa, Canada
2Jacobs-Universität Bremen, Germany
Groups, geometry, and dynamics, Tome 11 (2017) no. 1, pp. 57-74

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DOI

Let F be a non-Archimedean local field with the ring of integers O and the prime ideal p and let G=Gad​(O/pn) be the adjoint Chevalley group. Let mf​(G) denote the smallest possible dimension of a faithful representation of G. Using the Stone–von Neumann theorem, we determine a lower bound for mf​(G) which is asymptotically the same as the results of Landazuri, Seitz and Zalesskii for split Chevalley groups over Fq​. Our result yields a conceptual explanation of the exponents that appear in the aforementioned results.
DOI : 10.4171/ggd/387
Classification : 20-XX
Mots-clés : Chevalley groups, faithful representation, Heisenberg subgroups, local fields, Stone–von Neumann theorem

Mohammad Bardestani  1   ; Camelia Karimianpour  1   ; Keivan Mallahi-Karai  2   ; Hadi Salmasian  1

1 University of Ottawa, Canada
2 Jacobs-Universität Bremen, Germany 
Mohammad Bardestani; Camelia Karimianpour; Keivan Mallahi-Karai; Hadi Salmasian. Faithful representations of Chevalley groups over quotient rings of non-Archimedean local fields. Groups, geometry, and dynamics, Tome 11 (2017) no. 1, pp. 57-74. doi: 10.4171/ggd/387
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     author = {Mohammad Bardestani and Camelia Karimianpour and Keivan Mallahi-Karai and Hadi Salmasian},
     title = {Faithful representations of {Chevalley} groups over quotient rings of {non-Archimedean} local fields},
     journal = {Groups, geometry, and dynamics},
     pages = {57--74},
     year = {2017},
     volume = {11},
     number = {1},
     doi = {10.4171/ggd/387},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/387/}
}
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