Decomposition of some Witten-Reshetikhin-Turaev Representations into Irreducible Factors

Abstract

We decompose into irreducible factors the SU(2) Witten-Reshetikhin-Turaev representations of the mapping class group of a genus 2 surface when the level is p=4r and p=2r² with r an odd prime, and when p=2r₁r₂ with r₁, r₂ two distinct odd primes. Some partial generalizations in higher genus are also presented.