Abstract
We endow a non-semisimple category of modules of unrolled quantum \({\mathfrak {sl}(2)}\) with a Hermitian structure. We also prove that the CGP TQFT constructed in arXiv:1202.3553 using this category is Hermitian. This gives rise to projective representations of the mapping class group in the group of indefinite unitary matrices.
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Notes
We use an equivalent definition to the one Turaev uses for \({\mathop {{\text {ev}}}\limits ^{\longrightarrow }}_V^{\dagger }\).
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Acknowledgements
N.G. is supported by NSF DMS-1664387. A.D.L. is partially supported by NSF Grant DMS-1902092 and Army Research Office W911NF-20-1-0075. J.S. is partially supported by the NSF Grant DMS-1807161 and PSC CUNY Award 64012-00 52.
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Geer, N., Lauda, A.D., Patureau-Mirand, B. et al. A Hermitian TQFT from a non-semisimple category of quantum \({\mathfrak {sl}(2)}\)-modules. Lett Math Phys 112, 74 (2022). https://doi.org/10.1007/s11005-022-01570-x
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DOI: https://doi.org/10.1007/s11005-022-01570-x