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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Local cohomology and the multi-graded regularity of FI$^m$-modules
Liping Li,Eric Ramos +1 more
TL;DR: In this article, a local cohomology theory for FI$m$-modules over Cox rings was developed, which in many ways mimics the classical theory for multi-graded modules over a polynomial ring.
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Homology of the braid group with coefficients in the reduced Burau representation
TL;DR: The reduced Burau representation of the braid group is obtained from the homology of an infinite cyclic cover of the $n$-punctured disc in this article.
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Homological stability of topological moduli spaces
TL;DR: In this paper, the authors introduce the notion of twisted homology groups and derive twisted homological stability results for moduli spaces of high-dimensional manifolds and unordered configuration spaces of manifolds with labels in a fibration.
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The Structure of the Grothendieck Rings of Wreath Product Deligne Categories and their Generalisations
TL;DR: In this article, it was shown that the Grothendieck rings of these wreath product categories stabilise in some sense as $n \to \infty, where n is the number of vertices in a tensor category.
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Secondary characteristic classes for subgroups of automorphism groups of free groups
TL;DR: In this paper, the Borel regulator classes vanish on various groups related to various groups of free groups and the authors define three series of secondary characteristic classes for subgroups of automorphism groups.
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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.