Geodesic
Asymptotic faithfulness of the quantum SU(n) representations of the mapping class groups
Jørgen Ellegaard Andersen1
1 Institut for Matematiske Fag, Aarhus Universitet, 8000 Aarhus, Denmark
Annals of mathematics, Tome 163 (2006) no. 1, pp. 347-368.

Voir la notice de l'article provenant de la source Annals of Mathematics website

We prove that the sequence of projective quantum ${\rm SU}(n)$ representations of the mapping class group of a closed oriented surface, obtained from the projective flat ${\rm SU}(n)$-Verlinde bundles over Teichmüller space, is asymptotically faithful. That is, the intersection over all levels of the kernels of these representations is trivial, whenever the genus is at least $3$. For the genus $2$ case, this intersection is exactly the order $2$ subgroup, generated by the hyper-elliptic involution, in the case of even degree and $n=2$. Otherwise the intersection is also trivial in the genus $2$ case.
DOI : 10.4007/annals.2006.163.347

Jørgen Ellegaard Andersen 1

1 Institut for Matematiske Fag, Aarhus Universitet, 8000 Aarhus, Denmark 
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Jørgen Ellegaard Andersen. Asymptotic faithfulness of the quantum SU(n) representations of the mapping class groups. Annals of mathematics, Tome 163 (2006) no. 1, pp. 347-368. doi : 10.4007/annals.2006.163.347. http://geodesic.mathdoc.fr/articles/10.4007/annals.2006.163.347/

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