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On the asymptotics of quantum SU(2) representations of mapping class groups
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Michael Freedman
Published/Copyright:
May 17, 2006
Abstract
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,ℤ) on L2(ℝ). As a consequence we obtain a curious analytic fact about the Fourier transform on ℝ which may not have been previously observed.
Revised: 2004-09-28
Published Online: 2006-05-17
Published in Print: 2006-03-21
© Walter de Gruyter
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Articles in the same Issue
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Restricting isotropic α-stable Lévy processes from
to fractal sets - Continuous control and the algebraic L-theory assembly map
- Tilting modules and Gorenstein rings
- Variational character of the Cauchy-Riemann equations
- The Lp–Lq version of Hardy's Theorem on nilpotent Lie groups
- On the Lipschitz regularity for certain elliptic problems
- On the asymptotics of quantum SU(2) representations of mapping class groups
- Infinite-dimensional homotopy space forms
- Factor theorems for locally compact Markov shifts II
