We introduce the idea of representation stability (and several variations) for a sequence of
representations V n of groups G n. A central application of the new viewpoint we introduce …

FI-modules were introduced by the first three authors to encode sequences of
representations of symmetric groups. Over a field of characteristic 0, finite generation of an FI …

Given a family of groups admitting a braided monoidal structure (satisfying mild
assumptions) we construct a family of spaces on which the groups act and whose …

We study analogues of FI-modules where the role of the symmetric group is played by the
general linear groups and the symplectic groups over finite rings, and we prove basic …

We prove an explicit and sharp upper bound for the Castelnuovo–Mumford regularity of an
FI-module in terms of the degrees of its generators and relations. We use this to refine a …

We prove a homological stability theorem for families of discrete groups (eg mapping class
groups, automorphism groups of free groups, braid groups) with coefficients in a sequence …

A MODULE STRUCTURE ON CERTAIN ORBIT SETS OF UNIMODULAR ROWS Page 1
Journal of Pure and Applied Algebra 57 (1989) 281-316 North-Holland 281 A MODULE …

In 1977, Vogtmann[lo] proved that the groups O,.(k) are homology stable for any field k, k#[F,.
That is, the natural homomorphisms H;(O,.(k); Z)-+ H;(O n+ I, n+ i (k); Z) are isomorphisms for …

The homology groups of many natural sequences of groups {G_n\} _ n= 1^ ∞ G nn= 1∞(eg
general linear groups, mapping class groups, etc.) stabilize as n → ∞ n→∞. Indeed, there is …

Representation stability is a phenomenon whereby the structure of certain sequences $ X_n
$ of spaces can be seen to stabilize when viewed through the lens of representation theory …