An expansion of the Jones representation of genus 2 and the Torelli group II

We continue to study the algebraic property of the linear representation of the mapping class group of a closed oriented surface of genus 2 constructed by V. F. R. Jones. We consider the perturbation of the representation at the involved parameter t = 1. This perturbation naturally induces a filtration on the Torelli group which is coarser than its. lower central series. We present some results on the structure of the associated graded quotients. Our arguments follow the same line of our previous paper which dealt with the perturbation at t = -1. However, the obtained results may still suggest a new aspect of the representation.