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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FI-modules and the cohomology of modular representations of symmetric groups
TL;DR: In this paper, it was shown that for a "finitely generated" FI-module over a field of characteristic $p, the cohomology groups are eventually periodic in $n.
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Stability in the homology of congruence subgroups
TL;DR: In this article, it was shown that the homology groups of congruence subgroups satisfy a strong version of representation stability, called central stability, which is defined via a universal property.
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A spectral sequence for stratified spaces and configuration spaces of points
TL;DR: In this paper, a spectral sequence associated to a stratified space is constructed, which computes the compactly supported cohomology groups of an open stratum in terms of the closed strata and the reduced cohomologies groups of the poset of strata.
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FI_W-modules and stability criteria for representations of the classical Weyl groups
TL;DR: In this article, the authors present an algebraic framework for studying sequences of representations of any of the three families of classical Weyl groups, extending work of Church, Ellenberg, Farb, and Nagpal on the symmetric groups S_n to the signed permutation groups B_n and D_n. The theory of FI_W-modules gives a conceptual framework for stability results such as these.
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Symmetric group characters as symmetric functions
Rosa Orellana,Mike Zabrocki +1 more
TL;DR: In this article, a basis of symmetric functions that evaluates to the irreducible characters of the symmetric group was introduced, and three different characterizations for this basis were given.
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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.
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Sur La Cohomologie des Espaces Fibres Principaux et des Espaces Homogenes de Groupes de Lie Compacts
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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.