Projective representations of Hecke groups from Topological quantum field theory

Yuze Ruan

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arXiv · 2203.10745

Projective representations of Hecke groups from Topological quantum field theory

Yuze Ruan

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Abstract

We construct projective (unitary) representations of Hecke groups from the vector spaces associated with the Witten-Reshetikhin-Turaev topological quantum field theory of higher genus surfaces. In particular, we generalize the modular data of Temperley-Lieb-Jones modular categories. We also study some properties of the representation. We show the image group of the representation is infinite at low levels in genus $2$ by explicit computations. We also show the representation is reducible with at least three irreducible summands when the level equals $4l+2$ for $l\geq 1$.

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BibTeX RIS

Yuze Ruan. 2022-03-21. Projective representations of Hecke groups from Topological quantum field theory. https://arxiv.org/abs/2203.10745

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