Linear representations of random groups

2018/10/02 by Kozma, Gady, Lubotzky, Alexander
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1810.01529

Abstract

We show that for a fixed k, Gromov random groups with any positive density have no non-trivial degree-k representations over any field, a.a.s. This is especially interesting in light of the results of Agol, Ollivier and Wise that when the density is less than 1/6 such groups have a faithful linear representation over the rationals, a.a.s.

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