On Integrality of Non-Semisimple Quantum Representations of Mapping Class Groups

• DOI: 10.48550/arxiv.2407.20644
• Publication Date: 2024-08-22
• Authors: Marco De Renzi; Jules Martel
• Keywords: Root of unity

For a root of unity $\zeta$ odd prime order, we restrict coefficients non-semisimple quantum representations mapping class groups associated with the small group $\mathfrak{u}_\zeta \mathfrak{sl}_2$ from $\mathbb{Q}(\zeta)$ to $\mathbb{Z}[\zeta]$. We do this by exhibiting explicit bases states spaces that span $\mathbb{Z}[\zeta]$-lattices are invariant under projective actions groups.