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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Word Measures on Symmetric Groups
Liam Hanany,Doron Puder +1 more
TL;DR: In this article, it was shown that the average number of fixed points in a $w$-random permutation in a symmetric group with random generators is at most O(n 2r-1+O(N^{1-\pi\left(w\right)}\right)$, where σ is the smallest rank of a subgroup of a group.
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Koszulity of directed categories in representation stability theory
Wee Liang Gan,Liping Li +1 more
TL;DR: In this article, it was shown that infinite directed categories in the theory of representation stability are Koszul over a field of characteristic zero, and a general criterion for an infinite directed category to be a k-category is given.
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Representation stability for the cohomology of arrangements associated to root systems
Christin Bibby,Christin Bibby +1 more
TL;DR: In this paper, it was shown that the rational cohomology stabilizes as a sequence of Weyl group representations, based on a combinatorial description of the poset of connected components of intersections of subvarieties in the arrangement.
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Homology of braid groups, the Burau representation, and $\mathbb{F}_q$-points on superelliptic curves
TL;DR: In this article, the reduced Burau representation of the braid group with coefficients in the complexified reducedBurau representation is derived from the homology of an infinite cyclic cover of the disc with punctures.
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A comparison of twisted coefficient systems
TL;DR: In this paper, the authors review and compare various instances of the notion of twisted coefficient system, a.k.a. polynomial functor, appearing in the literature, and explain a functorial framework for this setting.
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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.