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.
References
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Parametrized Abel-Jacobi maps and abelian cycles in the Torelli group
Thomas Church,Benson Farb +1 more
TL;DR: In this article, it was shown that tau_i is not injective (even rationally) for any 2 = 3, and that the Torelli group is nonzero for each 1 = 1.
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Towards representation stability for the second homology of the Torelli group
TL;DR: In this article, the second homology group of the Torelli group of a surface of genus g and 1 boundary component is generated as an Sp(2g,Z)-module by the image under the stabilization map of the secondhomology group.
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Representation stability for syzygies of line bundles on Segre--Veronese varieties
TL;DR: In this article, it was shown that the multivariate version of representation stability, a notion recently introduced and studied by Church and Farb, holds for the homology groups of packing complexes, which allows us to deduce stability properties for the syzygies of line bundles on Segre-Veronese varieties.
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The cohomology of the cotangent bundle of Heisenberg groups
Leandro Cagliero,Paulo Tirao +1 more
TL;DR: In this article, the full module structure of the cohomology group of the Heisenberg Lie algebra with exterior adjoint coefficients is determined explicitly, over the symplectic group.