Asymptotic faithfulness of the quantum SU(n) representations of the mapping class groups
By J. Andersen. 2002
143 citations recorded by the source corpus.
We prove that the sequence of projective quantum SU(n) representations of the mapping class group of a closed oriented surface, obtained from the projective flat SU(n)-Verlinde bundles over Teichm?uller 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.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/b6db97eba10e8f93d5efabbda93142ba18e0a4a9
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In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Reshetikhin-Turaev invariants of Seifert 3-manifolds for classical simple Lie algebras, and their asymptotic expansions (2002, methodology): “The proof involves asymptotics of Hitchin’s connection over Teichmüller space, approximations to all orders, of the boundary states of handle bodies and techniques similar to the ones presented in [3].”