# ALGEBRAIC COMBINATORICS

Representation stability on the cohomology of complements of subspace arrangements
Algebraic Combinatorics, Volume 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 ${S}_{n}$-modules. We consider arrangements of linear subspaces defined by sets of diagonal equalities ${x}_{i}={x}_{j}$ and invariant under the action of ${S}_{n}$ 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.

Revised:
Accepted:
Published online:
DOI: 10.5802/alco.60
Classification: 55-XX,  05E10
Keywords: representation stability, subspace arrangement, symmetric functions
Rapp, Artur 1

1 Philipps-Universität Marburg Fachbereich Mathematik und Informatik Hans-Meerweinstr. 6 35032 Marburg, Germany
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Rapp, Artur. Representation stability on the cohomology of complements of subspace arrangements. Algebraic Combinatorics, Volume 2 (2019) no. 4, pp. 603-611. doi : 10.5802/alco.60. https://alco.centre-mersenne.org/articles/10.5802/alco.60/

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