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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The homology of the Brauer algebras
TL;DR: In this paper, the homology of Brauer algebras, interpreted as appropriate Tor-groups, was investigated and it was shown that it is closely related to the symmetric group.
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The Hopf structure of symmetric group characters as symmetric functions
Rosa Orellana,Mike Zabrocki +1 more
TL;DR: In this article, the authors introduced inhomogeneous bases of the ring of symmetric functions and proved product and coproduct formulae for these bases, and gave the transition coefficients between the elementary symmetric function and the irreducible character basis.
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$\mathrm{FI}_G$-modules, orbit configuration spaces, and complex reflection groups
TL;DR: The notion of character polynomials was first defined and explored by Church-Ellenberg-Farb and Wilson as mentioned in this paper, who developed a notion of representation stability which they called $K_0$-stability even when $G$ is infinite virtually polycyclic.
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Representation stability, secondary stability, and polynomial functors.
TL;DR: In this article, a general representation stability result for polynomial coefficient systems with twisted coefficients was proved, which gave two generalizations of classical homological stability theorems for twisted coefficients.
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Splitting behavior of S n -polynomials
TL;DR: For a fixed finite set of primes S, this article analyzed the probability that a random, monic, degree n polynomial with coefficients in a box of side B satisfies: (i) f(x) is irreducible over Open image in new window, with splitting field with Galois group Sn; (ii) Disc(f) is relatively prime to all primes in S; and (iii) f (x) has a prescribed splitting type at each prime p in S.
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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.