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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Étale homological stability and arithmetic statistics
Benson Farb,Jesse Wolfson +1 more
TL;DR: In this article, the authors contribute to the arithmetic/topology dictionary by relating asymptotic point counts and arithmetic statistics over finite fields to homological stability and representation stability over smooth varieties.
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Stable decompositions of certain representations of the finite general linear groups
Wee Liang Gan,John Watterlond +1 more
TL;DR: In this paper, it was shown that the irreducible decomposition of the permutation representation of GLn stabilizes for large n for finitely generated VIC-modules.
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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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Stability in the homology of Deligne-Mumford compactifications
TL;DR: In this article, the authors studied the asymptotic behavior of the homology of the Deligne-Mumford compactification of the moduli space of curves and bound the degree of generation of FS^op modules.
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Homological stability for moduli spaces of disconnected submanifolds, I
TL;DR: In this article, the authors generalize this result to moduli spaces of submanifolds of higher dimension, where stability is with respect to the number of components having a fixed diffeomorphism type and isotopy class.
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
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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.