Representation theory and homological stability
Thomas Church,Benson Farb +1 more
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TLDR
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 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.
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GL-equivariant modules over polynomial rings in infinitely many variables
TL;DR: In this paper, the authors define and prove finiteness properties for analogues of Hilbert series, systems of parameters, depth, local cohomology, Koszul duality, and regularity.
Posted Content
The tropicalization of the moduli space of curves
TL;DR: In this article, the skeleton of the Deligne-Mumford-Knudsen moduli stack of stable curves is naturally identified with the moduli space of extended tropical curves, and this is compatible with the "naive" set-theoretic tropicalization map.
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Homological stability for automorphism groups
TL;DR: In this paper, a family of groups admitting a braided monoidal structure is constructed, and the authors show that homological stability holds with both polynomial and abelian twisted coefficients, with no further assumptions.
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Homological stability for configuration spaces of manifolds
TL;DR: In this paper, it was shown that certain sequences of induced representations are monotone, and the notion of monotonicity was introduced for a sequence of S-n representations, which is of independent interest.
References
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Book
Representation Theory: A First Course
TL;DR: This volume represents a series of lectures which aims to introduce the beginner to the finite dimensional representations of Lie groups and Lie algebras.
BookDOI
Discrete subgroups of semisimple Lie groups
TL;DR: The Structure of the Book as discussed by the authors is a collection of essays about algebraic groups over arbitrary fields, including a discussion of the relation between the structure of closed subgroups and property (T) of normal subgroups.
Journal ArticleDOI
Sur La Cohomologie des Espaces Fibres Principaux et des Espaces Homogenes de Groupes de Lie Compacts
Book
Young Tableaux: With Applications to Representation Theory and Geometry
TL;DR: In this paper, the authors introduce the notion of the plactic monoid in the calculus of tableux and show that it can be represented by a symmetric polynomials.
Book
Free Lie Algebras
TL;DR: In this article, it was shown that the Lie algebra of Lie polynomials is the free Lie algebra, and that its enveloping algebra is the associative algebra of noncommutative polynomorphisms.