Asymptotic faithfulness of the quantum SU(n) representations of the mapping class groups
Asymptotic faithfulness of the quantum SU(n) representations of the mapping class groups
复制标题
映射类群的量子 SU(n) 表示的渐近忠实度
DOI：
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发表时间：
2002
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通讯作者：
J. Andersen
中科院分区：
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作者：
J. Andersen
我们证明了由Teichm上的投射平坦SU（n）-Verlinde丛得到的闭定向曲面的映射类群的投射量子SU（n）表示序列是等价的。Uller空间是渐近忠实的。也就是说，只要亏格至少为3，这些表示的核的所有水平上的交集都是平凡的。对于亏格2的情形，这个交恰好是由超椭圆对合生成的2阶子群，在偶数次和n = 2的情形下。否则在亏格2的情况下交也是平凡的。
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.