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- W2508211770 abstract "We show, finitely generated rational $$mathsf {VIC}_mathbb Q$$ -modules and $$mathsf {SI}_mathbb Q$$ -modules are uniformly representation stable and all their submodules are finitely generated. We use this to prove two conjectures of Church and Farb, which state that the quotients of the lower central series of the Torelli subgroups of $${{mathrm{Aut}}}(F_n)$$ and $${{mathrm{Mod,}}}(Sigma _{g,1})$$ are uniformly representation stable as sequences of representations of the general linear groups and the symplectic groups, respectively. Furthermore we prove an analogous statement for their Johnson filtrations." @default.
- W2508211770 created "2016-09-16" @default.
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- W2508211770 date "2018-06-11" @default.
- W2508211770 modified "2023-10-15" @default.
- W2508211770 title "Representation stability for filtrations of Torelli groups" @default.
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- W2508211770 doi "https://doi.org/10.1007/s00208-018-1708-6" @default.
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