Representation stability for filtrations of Torelli groups

We show, finitely generated rational VIC Q -modules and SI 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 A...

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Bibliographic Details
Published inMathematische annalen Vol. 372; no. 1-2; pp. 257 - 298
Main Author Patzt, Peter
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2018
Springer Nature B.V
Subjects
Mathematics
Mathematics and Statistics
Modules
Quotients
Representations
Sequences
Subgroups
Primary 20G05
20F40
58D05
Secondary 20E36
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Summary:We show, finitely generated rational VIC Q -modules and SI 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 Aut ( F n ) and Mod ( Σ 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.
ISSN:0025-5831
1432-1807
DOI:10.1007/s00208-018-1708-6