Representation theory and homological stability
Thomas Church,Benson Farb +1 more
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In this article, the authors introduce the idea of representation stability for a sequence of representations V n of groups G n, and apply it to counting problems in number theory and finite group theory.About:
This article is published in Advances in Mathematics.The article was published on 2013-10-01 and is currently open access. It has received 274 citations till now. The article focuses on the topics: Representation theory of finite groups & Trivial representation.read more
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FI-modules and stability for representations of symmetric groups
TL;DR: The theory of FI-modules was introduced and developed in this paper, and it is shown that for any fixed degree the character is given, for n large enough, by a polynomial in the cycle-counting functions that is independent of n.
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FI-modules and stability for representations of symmetric groups
TL;DR: The theory of FI-modules is introduced and developed in this paper, where the authors show that for any fixed degree the character is given, for n large enough, by a polynomial in the cycle-counting functions that is independent of n.
Journal ArticleDOI
Gr\"obner methods for representations of combinatorial categories
Steven V Sam,Andrew Snowden +1 more
TL;DR: In this article, the authors studied how the combinatorial behavior of a category C affects the algebraic behavior of representations of C, and showed that C-algebraic representations are noetherian.
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Gröbner methods for representations of combinatorial categories
TL;DR: In this article, the authors studied how the combinatorial behavior of a category C affects the algebraic behavior of representations of C, and showed that C-algebraic representations are noetherian.
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FI-modules over Noetherian rings
TL;DR: The Noetherian property of FI-modules was shown in this paper, where it was shown that for any sub-FI-module of a finitely generated FI-module, the representation stability of the corresponding sequence of Sn-representations is guaranteed.
References
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Proceedings ArticleDOI
Structure of the mapping class groups of surfaces: a survey and a prospect
TL;DR: In this paper, the authors survey recent works on the structure of the mapping class groups of surfaces mainly from the point of view of topology, and discuss several possible directions for future research.
Book
Modular Representations of Finite Groups of Lie Type
TL;DR: The representation theory of finite groups of Lie type over a field of defining prime characteristic has been studied intensively for half a century as discussed by the authors, though some key problems remain unsolved, and the relationship between ordinary and modular representations is explored in the context of Deligne-Lusztig characters.
Journal ArticleDOI
On the descending central series of groups with a single defining relation
TL;DR: In this paper, it was shown that the Lie algebra associated to the descending central series of a finitely generated group with a single primitive defining relation is a Lie algebra with a defining relation.
Posted Content
Cohomological aspects of magnus expansions.
TL;DR: In this article, the authors generalize the notion of a Magnus expansion of a free group in order to extend each of the Johnson homomorphisms defined on a decreasing filtration of the Torelli group for a surface with one boundary component to the whole of the automorphism group Aut(Fn).
Journal ArticleDOI
FI-modules over Noetherian rings
TL;DR: The Noetherian property of FI-modules was shown in this paper, where it was shown that for any sub-FI-module of a finitely generated FI-module, the representation stability of the corresponding sequence of S_n-representations is guaranteed.