Images of Real Representations of $SL_n(Z_p)$

Abstract

In this paper, we investigate abstract homomorphism from the special linear group over complete discrete valuation rings with finite residue field, such as the ring of p-adic integers, into the general linear group over the reals. We find the minimal dimension in which such a representation has infinite image. For positive characteristic rings, this minimum is infinity.Comment: 10 pages, corrected typos and simplified the proof