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arXiv · 1810.01529

Linear representations of random groups

Gady Kozma·Alexander Lubotzky
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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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Gady Kozma, Alexander Lubotzky. 2018-10-02. Linear representations of random groups. https://arxiv.org/abs/1810.01529

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