Representation stability on the cohomology of complements of subspace arrangements
Rapp, Artur1
1 Philipps-Universität Marburg Fachbereich Mathematik und Informatik Hans-Meerweinstr. 6 35032 Marburg, Germany
Algebraic Combinatorics, Tome 2 (2019) no. 4, pp. 603-611.

We study representation stability in the sense of Church and Farb of sequences of cohomology groups of complements of arrangements of linear subspaces in real and complex space as Sn-modules. We consider arrangements of linear subspaces defined by sets of diagonal equalities xi=xj and invariant under the action of Sn which permutes the coordinates. We provide bounds for the point when stabilization occurs and an alternative proof of the fact that stabilization happens. The latter is a special case of very general stabilization results proved independently by Gadish and by Petersen; for the pure braid space the result is part of the work of Church and Farb. For the latter space, better stabilization bounds were obtained by Hersh and Reiner.

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DOI : 10.5802/alco.60
Classification : 55-XX, 05E10
Mots-clés : representation stability, subspace arrangement, symmetric functions
Rapp, Artur 1

1 Philipps-Universität Marburg Fachbereich Mathematik und Informatik Hans-Meerweinstr. 6 35032 Marburg, Germany 
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Rapp, Artur. Representation stability on the cohomology of complements of subspace arrangements. Algebraic Combinatorics, Tome 2 (2019) no. 4, pp. 603-611. doi : 10.5802/alco.60. https://www.numdam.org/articles/10.5802/alco.60/

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