Projective representations of Hecke groups from Topological quantum field theory

Fuente: arXiv
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Autore principale: Ruan, Yuze
Natura: Preprint
Pubblicazione: 2022
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_version_ 1866912133090902016
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