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

Abstract

For every irreducible complex representation π λ of the symmetric group S 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 S n ), has a natural description in terms of invariant subspaces of Young subgroups, and enjoys a number of remarkable properties.