Irreducible factors of modular representations of mapping class groups arising in integral TQFT (Q407399)

For a surface \(\Sigma\) which is closed or which has one boundary component, the paper under review investigates a modular representation \(F(\Sigma)\) of the mapping class group of \(\Sigma\) induced by an integral version of the Witten--Reshetikhin--Turaev \(SO(3)\) TQFT at the \(p\)th root of unity where \(p\) is an odd prime. They prove that \(F(\Sigma)\) has a composition series with at most \(2\) irreducible factors (Corrolary 2.6) whose dimensions are given by Verline-type formulae (Theorem 2.7). The authors remark that these formulae should also be investigated from a geometric perspective.