Asymptotic faithfulness of the quantum SU(n) representations of the mapping class groups
Annals of mathematics, Tome 163 (2006) no. 1, pp. 347-368
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.
@article{10_4007_annals_2006_163_347,
author = {J{\o}rgen Ellegaard Andersen},
title = {Asymptotic faithfulness of the quantum {SU(n)} representations of the mapping class groups},
journal = {Annals of mathematics},
pages = {347--368},
year = {2006},
volume = {163},
number = {1},
doi = {10.4007/annals.2006.163.347},
mrnumber = {2195137},
zbl = {1157.53049},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4007/annals.2006.163.347/}
}
TY - JOUR AU - Jørgen Ellegaard Andersen TI - Asymptotic faithfulness of the quantum SU(n) representations of the mapping class groups JO - Annals of mathematics PY - 2006 SP - 347 EP - 368 VL - 163 IS - 1 UR - http://geodesic.mathdoc.fr/articles/10.4007/annals.2006.163.347/ DO - 10.4007/annals.2006.163.347 LA - en ID - 10_4007_annals_2006_163_347 ER -
%0 Journal Article %A Jørgen Ellegaard Andersen %T Asymptotic faithfulness of the quantum SU(n) representations of the mapping class groups %J Annals of mathematics %D 2006 %P 347-368 %V 163 %N 1 %U http://geodesic.mathdoc.fr/articles/10.4007/annals.2006.163.347/ %R 10.4007/annals.2006.163.347 %G en %F 10_4007_annals_2006_163_347
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
Cité par Sources :