Free subgroups within the images of quantum representations

TL;DR

This paper proves that most quantum representations of Johnson subgroups of the mapping class group contain explicit free non-abelian subgroups, revealing new algebraic structures within these images.

Contribution

It establishes the presence of explicit free non-abelian subgroups in quantum images of Johnson subgroups, except for specific roots of unity.

Findings

Quantum images of Johnson subgroups contain free non-abelian subgroups.

The result holds for all roots of unity except a few explicit cases.

Provides new insights into the algebraic structure of quantum representations.

Abstract

We prove that, except for a few explicit roots of unity, the quantum image of any Johnson subgroup of the mapping class group contains an explicit free non-abelian subgroup.