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ON IMAGES OF REAL REPRESENTATIONS OF SPECIAL LINEAR GROUPS OVER COMPLETE DISCRETE VALUATION RINGS

  • TALIA FERNÓS (a1) and POOJA SINGLA (a2)

Abstract

In this paper, we investigate the abstract homomorphisms of the special linear group SLn( $\mathfrak{O}$ ) over complete discrete valuation rings with finite residue field into the general linear group GLm( $\mathbb{R}$ ) over the field of real numbers. We show that for m < 2n, every such homomorphism factors through a finite index subgroup of SLn( $\mathfrak{O}$ ). For $\mathfrak{O}$ with positive characteristic, this result holds for all m ${\mathbb N}$ .

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ON IMAGES OF REAL REPRESENTATIONS OF SPECIAL LINEAR GROUPS OVER COMPLETE DISCRETE VALUATION RINGS

  • TALIA FERNÓS (a1) and POOJA SINGLA (a2)

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