Introducing the notion of FI-modules (-representations):
Thomas Church, Jordan S. Ellenberg, Benson Farb, FI-modules and stability for representations of symmetric groups, Duke Math. J. 164 9 (2015) 1833-1910 [arXiv:1204.4533, doi:10.1215/00127094-3120274]
Thomas Church, Jordan S. Ellenberg, Benson Farb, Rohit Nagpal, FI-modules over Noetherian rings, Geom. Topol. 18 (2014) 2951-2984 [arXiv:1210.1854, doi:10.2140/gt.2014.18.2951]
and the notion of representation stability:
245 (2013) 250-314 [doi:10.1016/j.aim.2013.06.016]
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