Faithful representations of Chevalley groups over quotient rings of\n non-Archimedean local fields

2014/03/14 by Mohammad Bardestani, Bardestani, Mohammad, Camelia Karimianpour +5
Mathematics · #Advanced Algebra and Geometry #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1403.3722

openalex publication_date 2014/03/14 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

Let F be a non-Archimedean local field with the ring of integers\n\O and the prime ideal mathfrakp and let G= bf\nG\(\O/ mathfrakpⁿ\) be the adjoint Chevalley group. Let\nm_f(G) denote the smallest possible dimension of a faithful representation of\nG. Using the Stone-von Neumann theorem, we determine a lower bound for\nm_f(G) which is asymptotically the same as the results of Landazuri, Seitz\nand Zalesskii for split Chevalley groups over mathbbF_q. Our result yields\na conceptual explanation of the exponents that appear in the aforementioned\nresults\n

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