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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On the growth of the Kronecker coefficients
TL;DR: In this article, the authors study the rate of growth experienced by the Kronecker coefficients as they add cells to the rows and columns indexing partitions, and they do this by moving to the setting of the reduced KCC coefficients.
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Generalized Representation Stability and FI_d-modules
TL;DR: In this article, the authors consider the complex representation theory of FI_d, a natural generalization of the category FI of finite sets and injections, and prove that finitely generated FI-d-modules exhibit behaviors in the spirit of Church-Farb representation stability theory, generalizing a theorem of Church, Ellenberg and Farb which connects finite generation of FI-modules to representation stability.
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Twisted homological stability for configuration spaces
TL;DR: In this paper, it was shown that the sequence of configuration spaces of n unordered, distinct points in M is homologically stable with coefficients in Z: in each degree, the integral homology is eventually independent of n. The result and the methods are generalisations of those of Betley for symmetric groups.
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Asymptotic behaviors of representations of graded categories with inductive functors
Wee Liang Gan,Liping Li +1 more
TL;DR: In this article, a sufficient criterion for finiteness of Castelnuovo-Mumford regularity of finitely generated representations of these categories is obtained, and a few important infinite combinatorial categories appearing in representation stability theory are equipped with inductive functors.
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Homological Stability for Spaces of Commuting Elements in Lie Groups
Daniel A. Ramras,Mentor Stafa +1 more
TL;DR: In this paper, it was shown that the rational homology of the space of unordered commuting $n$-tuples in a fixed group $G$ stabilizes as the number of commuting tuples increases.
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.