Quasiparabolic Gelfand models for finite irreducible Coxeter groups and their canonical Hecke structures

Abstract

Quasiparabolic sets extend parabolic coset spaces while retaining a length filtration and natural Hecke algebra deformations. Gelfand models built from induced linear characters ask when such spaces can account for every irreducible representation exactly once. We classify, up to equality of the individual induced characters, all quasiparabolic Gelfand models for finite irreducible Coxeter groups with inducing characters restricted from their ambient parabolic subgroups, including the additional models of type \(D_{4r+2}\) and \(B_3\). We derive the associated finite Gelfand-pair and commutant consequences, construct canonical Hecke structures for the additional classical models.