The intrinsic hyperplane arrangement in an arbitrary irreducible representation of the symmetric group

2019/10/18 by Tsilevich, N., Vershik, A., Yuzvinsky, S.
#05E10 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1910.08302

Abstract

For every irreducible complex representation~π_λ of the symmetric group~§_n, we construct, in a canonical way, a so-called intrinsic hyperplane arrangement~\A_λ in the space of~π_λ. This arrangement is a direct generalization of the classical braid arrangement (which is the special case of our construction corresponding to the natural representation of~§_n), has a natural description in terms of invariant subspaces of Young subgroups, and enjoys a number of remarkable properties.

Related

• Representation stability in the intrinsic hyperplane arrangements associated to irreducible representations of the symmetric-groups
• Hyperplane arrangements and Vinberg's θ-groups
• Symmetry of f-vectors of toric arrangements in general position and some applications
• A natural representation model for symmetric groups
• Orbit configuration spaces associated to discrete subgroups of PSL(2,R)