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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A geometric approach to counting norms in cyclic extensions of function fields
TL;DR: In this paper, an explicit version of a function field analogue of a classical result of Odoni (Mathematika 22(1):71-80, 1975) about norms in number fields, in the case of a cyclic Galois extension, was proved.
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A quotient of Fomin-Kirillov Algebra and q-Lucas polynomial
TL;DR: In this article, a quotient of Fomin-Kirillov algebra over the ideal generated by the edges of a complete graph on n vertexes that are missing in the $n$-cycle graph $C_n$ was introduced.
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Motivic random variables and representation stability II: Hypersurface sections
TL;DR: In this article, the authors prove geometric and cohomological stabilization results for the universal smooth degree $d$ hypersurface section of a fixed smooth projective variety as the degree goes to infinity.
The ${\mathbb S}_n$-equivariant Euler characteristic of the moduli space of graphs
TL;DR: In this paper , a formula for the Euler characteristic of the moduli space of graphs was proposed, based on explicit computations using this formula, and it was shown that the dependence on the number of isomorphisms of a graph on a graph stabilizes for large numbers of vertices.
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Stability for Representations of Hecke Algebras of type $A$
Kun Wang,Haitao Ma,Zhu-Jun Zheng +2 more
TL;DR: In this paper, the stability of a sequence of modules over Hecke algebras has been studied, and it has been shown that a finitely generated consistent sequence associated with a hecke algebra is representation stable.
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.