Representation Stability in the Intrinsic Hyperplane Arrangements Associated to Irreducible Representations of the Symmetric Groups

Authors

• Ian Flynn, Portland State University
• Eric Ramos, Stevens Institute of Technology, Hoboken
• Benjamin Young, University of Oregon

Sponsor

Supported by NSF grant DMS-2137628.

Published In

arXiv

Document Type

Pre-Print

Publication Date

10-2026

Subjects

Hyperplane arrangements

Abstract

Some of the most classically relevant Hyperplane arrangements are the Braid Arrangements Bn and their associated compliment spaces Fn. In their recent work, Tsilevich, Vershik, and Yuzvinsky [TVY20] 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 compliment spaces to these intrinsic arrangements display behaviors far removed from Fn. 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.

Rights

Copyright (c) 2026 The Authors

Description

Pre-print

Persistent Identifier

https://archives.pdx.edu/ds/psu/45225

Citation Details

Flynn, I., Ramos, E., & Young, B. (2024). Representation stability in the intrinsic hyperplane arrangements associated to irreducible representations of the symmetric-groups. arXiv preprint arXiv:2405.13291.