Linear representations of random groups

Abstract

We show that for a fixed k ∈ ℕ, Gromov random groups with any density d > 0 have no nontrivial 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 d < 1 6 such groups have a faithful linear representation over ℚ, a.a.s.

Keywords

• random groups
• representations
• bezout theorem