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 -modules. We consider arrangements of linear subspaces defined by sets of diagonal equalities and invariant under the action of 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
Keywords: representation stability, subspace arrangement, symmetric functions
Rapp, Artur 1
@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}, zbl = {1427.55012}, mrnumber = {3997513}, language = {en}, url = {https://alco.centre-mersenne.org/articles/10.5802/alco.60/} }
TY - JOUR AU - Rapp, Artur TI - Representation stability on the cohomology of complements of subspace arrangements JO - Algebraic Combinatorics PY - 2019 SP - 603 EP - 611 VL - 2 IS - 4 PB - MathOA foundation UR - https://alco.centre-mersenne.org/articles/10.5802/alco.60/ DO - 10.5802/alco.60 LA - en ID - ALCO_2019__2_4_603_0 ER -
%0 Journal Article %A Rapp, Artur %T Representation stability on the cohomology of complements of subspace arrangements %J Algebraic Combinatorics %D 2019 %P 603-611 %V 2 %N 4 %I MathOA foundation %U https://alco.centre-mersenne.org/articles/10.5802/alco.60/ %R 10.5802/alco.60 %G en %F ALCO_2019__2_4_603_0
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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