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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Kazhdan-Lusztig polynomials of matroids: a survey of results and conjectures
TL;DR: In this paper, various results, conjectures, and open problems related to Kazhdan-Lusztig polynomials of matroids are reported, all of which appear here for the first time.
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Stability and periodicity in the modular representation theory of symmetric groups
TL;DR: In this paper, asymptotic properties of the modular representation theory of symmetric groups and modular analogs of stabilization phenomena in characteristic zero are investigated. But the main results are equivalences of categories between certain abelian subcategories of representations of representations for different $n$ and $m$ and apply these results to obtain a structural result for $FI$-modules.
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The equivariant Kazhdan-Lusztig polynomial of a matroid
TL;DR: In this paper, the equivariant Kazhdan-Lusztig polynomial of a matroid equipped with a group of symmetries was defined, generalizing the nonequivariant case.
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On the second homology group of the Torelli subgroup of Aut(F_n)
Matthew B. Day,Andrew Putman +1 more
TL;DR: In this article, a finite set of generators for the Torelli subgroup of Aut(F_n) is given for H_2(IA_n), where IA_n is a GL_n(Z)-module.
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Homological Invariants of FI-modules and FI_G-modules
TL;DR: In this article, the authors explore a theory of depth for finitely presented FI G -modules and provide bounds on the stable ranges of FI-modules, making effective a theorem of Nagpal and thereby refining the stable range in results of Church, Ellenberg, and Farb.
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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.