The Asymptotics of Quantum
نویسنده
چکیده
We investigate the rigidity and asymptotic properties of quantum SU(2) representations of mapping class groups. In particular we prove that the hyperelliptic mapping class groups do not have Kazhdan’s property (T). On the other hand, the quantum SU(2) 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,Z) on L(R). As a consequence we obtain a curious analytic fact about the Fourier transform on R which may not have been previously observed.
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تاریخ انتشار 2004