Representation theory and homological stability
Thomas Church,Benson Farb +1 more
Reads0
Chats0
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
Citations
More filters
Posted Content
Algebraic structures on cohomology of configuration spaces of manifolds with flows
TL;DR: In this article, it was shown that the cohomology group with coefficients in a field H^i(PConf^n M, k) is an N-module, where N is the category of noncommutative finite sets introduced by Pirashvili and Richter.
Journal ArticleDOI
The stable homology of congruence subgroups
TL;DR: In this article, the completed cohomology groups of SLN.OF /, where OF is the ring of integers of a number field, were compared to K-theory and Galois cohomologies.
Journal ArticleDOI
Representation stability for the cohomology of arrangements associated to root systems
Christin Bibby,Christin Bibby +1 more
TL;DR: In this article, it was shown that the rational cohomology stabilizes as a sequence of Weyl group representations, which is the case in the case of reflecting hyperplanes.
Journal ArticleDOI
On the second homology group of the Torelli subgroup of Aut(Fn)
Matthew B. Day,Andrew Putman +1 more
TL;DR: In this paper, the Torelli subgroup of AutpFnq is considered and a finite set of generators for H2pIAnq as a GLnpZq-module is given.
Posted Content
FI_W-modules and constraints on classical Weyl group characters
TL;DR: In this article, the authors studied the characters of sequences of representations of any of the three families of classical Weyl groups W_n: the symmetric groups, the signed permutation groups (hyperoctahedral groups), or the even-signed permutation group.
References
More filters
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.