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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Journal ArticleDOI
Representation Stability and Finite Orthogonal Groups
Arunchalam Kannan,Zilun Wang +1 more
TL;DR: In this paper , a homological stability theorem for orthogonal groups over finite commutative rings where 2 is a unit was proved for both untwisted and twisted coefficients.
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On computing the eventual behavior of an FI-module over the rational numbers
TL;DR: In this paper, the authors give a formula for the eventual multiplicities of irreducible representations appearing in a finitely-presented FI-module over the rational numbers, which relies on structure theory due to Sam-Snowden SS16.
Book ChapterDOI
The Cohomology of $$\mathcal{M}_{0,n}$$ as an FI-Module
TL;DR: In this paper, the authors revisited the cohomology groups of the moduli space of n-pointed curves of genus zero using the FI-module perspective introduced by Church-Ellenberg-Farb.
Journal ArticleDOI
The homology of the Brauer algebras
TL;DR: In this paper, the homology of the Brauer algebras was investigated and it was shown that it is closely related to the symmetric group, in a range of degrees that increases with n.
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A representation stability theorem for VI-modules
Wee Liang Gan,John Watterlond +1 more
TL;DR: In this paper, it was shown that the sequence obtained from any finitely generated VI-module over an algebraically closed field of characteristic zero is representation stable, i.e., it can be represented by a sequence of representations of the finite general linear groups.
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.