Projective representations of Hecke groups from Topological quantum field theory
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866912133090902016 |
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| author | Ruan, Yuze |
| author_facet | Ruan, Yuze |
| contents | 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 $l\geq 1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2203_10745 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Projective representations of Hecke groups from Topological quantum field theory Ruan, Yuze Geometric Topology Quantum Algebra Representation Theory 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 $l\geq 1$. |
| title | Projective representations of Hecke groups from Topological quantum field theory |
| topic | Geometric Topology Quantum Algebra Representation Theory |
| url | https://arxiv.org/abs/2203.10745 |