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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FI-modules and stability for representations of symmetric groups
TL;DR: The theory of FI-modules was introduced and developed in this paper, and it is shown that for any fixed degree the character is given, for n large enough, by a polynomial in the cycle-counting functions that is independent of n.
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FI-modules and stability for representations of symmetric groups
TL;DR: The theory of FI-modules is introduced and developed in this paper, where the authors show that for any fixed degree the character is given, for n large enough, by a polynomial in the cycle-counting functions that is independent of n.
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Gr\"obner methods for representations of combinatorial categories
Steven V Sam,Andrew Snowden +1 more
TL;DR: In this article, the authors studied how the combinatorial behavior of a category C affects the algebraic behavior of representations of C, and showed that C-algebraic representations are noetherian.
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Gröbner methods for representations of combinatorial categories
TL;DR: In this article, the authors studied how the combinatorial behavior of a category C affects the algebraic behavior of representations of C, and showed that C-algebraic representations are noetherian.
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FI-modules over Noetherian rings
TL;DR: The Noetherian property of FI-modules was shown in this paper, where it was shown that for any sub-FI-module of a finitely generated FI-module, the representation stability of the corresponding sequence of Sn-representations is guaranteed.
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The stability of the Kronecker product of Schur functions
TL;DR: In this article, it was shown that the Kronecker coefficients appearing in the product of two Schur functions of degree n do not depend on the first part of the indexing partitions, but only on the values of their remaining parts.
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Torelli Groups and Geometry of Moduli Spaces of Curves
TL;DR: In this article, Johnson's work on the first homology of the Torelli groups was applied to study the geometry of moduli spaces of curves, and the results on normal functions were used to prove generalizations of the Franchetta conjecture for curves and abelian varieties.
Torelli Groups and Geometry of Moduli Spaces of Curves
TL;DR: The Torelli group Tg is the group of isotopy classes of diffeomorphisms of a compact orientable surface of genus g that act trivially on the homology of the surface as discussed by the authors.
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The Picard group of the moduli space of curves with level structures
TL;DR: For 4∤L and g large, the integral Picard groups of the moduli spaces of curves and principally polarized abelian varieties with level L structures were derived in this article.