On the asymptotics of quantum SU(2) representations of mapping class groups

被引:9
|
作者
Freedman, M [1 ]
Krushkal, V
机构
[1] Microsoft Res, Redmond, WA 98052 USA
[2] Univ Virginia, Charlottesville, VA 22904 USA
基金
美国国家科学基金会;
关键词
D O I
10.1515/FORUM.2006.017
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We investigate the rigidity and asymptotic properties of quantum SU(2) representations of mapping class groups. In the spherical braid group case the trivial representation is not isolated in the family of quantum SU(2) representations. In particular, they may be used to give an explicit check that spherical braid groups and hyperelliptic mapping class groups do not have Kazhdan's property (T). On the other hand, the representations of the mapping class group of the torus do not have almost invariant vectors, in fact they converge to the metaplectic representation of SL(2,76) on L-2(R). As a consequence we obtain a curious analytic fact about the Fourier transform on R which may not have been previously observed. 2000 Mathematics Subject Classification.
引用
收藏
页码:293 / 304
页数:12
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