Geodesic
Representation stability and outer automorphism groups
Documenta mathematica, Tome 27 (2022), pp. 17-87.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

In this paper we study families of representations of the outer automorphism groups indexed on a collection of finite groups $\mathcal{U}$. We encode this large amount of data into a convenient abelian category which generalizes the category of VI-modules appearing in the representation theory of the finite general linear groups. Inspired by work of \textit{T. Church} et al. [Duke Math. J. 164, No. 9, 1833--1910 (2015; Zbl 1339.55004)], we investigate for which choices of $\mathcal{U}$ the abelian category is locally noetherian and deduce analogues of central stability and representation stability results in this setting. Finally, we show that some invariants coming from rational global homotopy theory exhibit representation stability.
Classification : 20J05, 05E10, 18A99, 20C99
Keywords: representation stability, local Noetherian abelian categories, rational global spectra 
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     author = {Pol, Luca and Strickland, Neil Patrick},
     title = {Representation stability and outer automorphism groups},
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Pol, Luca; Strickland, Neil Patrick. Representation stability and outer automorphism groups. Documenta mathematica, Tome 27 (2022), pp. 17-87. http://geodesic.mathdoc.fr/item/DOCMA_2022__27__a65/