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- W2098253227 abstract "We prove that, except for a few explicit roots of unity, the quantum image of any Johnson subgroup of the mapping class group contains an explicit free non-abelian subgroup. Our second result is that, in general, the images of quantum representations are not isomorphic to higher rank irreducible lattices in semi-simple Lie groups. In particular, when the the parameter p is an odd prime greater than or equal to 7, the images are subgroups of infinite index within the group of unitary matrices with cyclotomic integers entries. The proof consists in finding an infinite normal subgroup of infinite index in the image, which is impossible for higher rank irreducible lattices, according to Margulis. The same method also shows that the quantum images have finite index subgroups which surject onto Z. In particular, there exist finite index subgroups of mapping class groups with infinite abelianization." @default.
- W2098253227 created "2016-06-24" @default.
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- W2098253227 date "2011-08-24" @default.
- W2098253227 modified "2023-10-01" @default.
- W2098253227 title "Images of quantum representations and finite index subgroups of mapping class groups" @default.
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