# 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: https://doi.org/10.5802/alco.60
Classification: 55-XX,  05E10
Keywords: representation stability, subspace arrangement, symmetric functions
@article{ALCO_2019__2_4_603_0,
author = {Rapp, Artur},
title = {Representation stability on the cohomology of complements of subspace arrangements},
journal = {Algebraic Combinatorics},
pages = {603--611},
publisher = {MathOA foundation},
volume = {2},
number = {4},
year = {2019},
doi = {10.5802/alco.60},
mrnumber = {3997513},
zbl = {1427.55012},
language = {en},
url = {https://alco.centre-mersenne.org/articles/10.5802/alco.60/}
}
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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