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Representation Stability in the Intrinsic Hyperplane Arrangements Associated to Irreducible Representations of the Symmetric Groups
Flynn, Ian1; Ramos, Eric2; Young, Benjamin3
1Portland State University, Department of Mathematics and Statistics, Portland, OR, 97201
2Stevens Institute of Technology, Department of Mathematical Sciences, Hoboken NJ, 07030
3University of Oregon, Department of Mathematics, Eugene OR, 97401
Algebraic Combinatorics, Volume 9 (2026) no. 4, pp. 973-992

Some of the most classically relevant Hyperplane arrangements are the Braid Arrangements $B_n$ and their associated complement spaces $\mathcal{F}_n$. In their recent work, Tsilevich, Vershik, and Yuzvinsky [23] construct what they refer to as the intrinsic hyperplane arrangement within any irreducible representation of the symmetric group that generalize the classical braid arrangements. Through examples it is also shown that the associated complement spaces to these intrinsic arrangements display behaviors far removed from $\mathcal{F}_n$. In this work we study the intrinsic hyperplane arrangements of irreducible representations of the symmetric group from the perspective of representation stability. This work is both theoretical, proving representation stability theorems for hyperplane complements, as well as statistical, examining the outputs of a number of simulations designed to enumerate flats.

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Accepted:
Published online:
DOI: 10.5802/alco.498
Classification: 05E10, 52C35, 18A25
Keywords: Hyperplane Arrangements, Irreducible Representations of the Symmetric Groups, Representation Stability, Experimental Mathematics

Flynn, Ian  1 ; Ramos, Eric  2 ; Young, Benjamin  3

1 Portland State University, Department of Mathematics and Statistics, Portland, OR, 97201
2 Stevens Institute of Technology, Department of Mathematical Sciences, Hoboken NJ, 07030
3 University of Oregon, Department of Mathematics, Eugene OR, 97401
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
Flynn, Ian; Ramos, Eric; Young, Benjamin. Representation Stability in the Intrinsic Hyperplane Arrangements Associated to Irreducible Representations of the Symmetric Groups. Algebraic Combinatorics, Volume 9 (2026) no. 4, pp. 973-992. doi: 10.5802/alco.498
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