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Norm estimates and asymptotic faithfulness of the quantum SU(n) representations of the mapping class group

Journal article
Authors Xueyuan Wan
Genkai Zhang
Published in Geometriae Dedicata
ISSN 0046-5755
Publication year 2019
Published at Department of Mathematical Sciences
Language en
Links dx.doi.org/10.1007/s10711-019-00461...
Keywords Faithfulness, Mapping class group, Norm estimates, Peak sections, Representation
Subject categories Mathematics

Abstract

We give a direct proof for the asymptotic faithfulness of the quantum SU(n) representations of the mapping class group using peak sections in Kodaira embedding. We give also estimates on the norm of the parallell transport of the projective connection on the Verlinde bundle. The faithfulness has been proved earlier by J. E. Andersen using Toeplitz operators on compact Kähler manifolds and by J. Marché and M. Narimannejad using skein theory. © 2019, The Author(s).

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