有限不可约Coxeter群的拟抛物Gelfand模型及其典范Hecke结构
Quasiparabolic Gelfand models for finite irreducible Coxeter groups and their canonical Hecke structures
AI总结：
本文分类了有限不可约Coxeter群中由抛物子群诱导特征构造的拟抛物Gelfand模型，并推导了Gelfand对及典范Hecke结构。
AI中文摘要：
拟抛物集推广了抛物陪集空间，同时保留长度过滤和自然的Hecke代数形变。由诱导线性特征构造的Gelfand模型探讨此类空间何时能恰好一次地涵盖每个不可约表示。我们分类了所有有限不可约Coxeter群的拟抛物Gelfand模型，其中诱导特征限制自其环境抛物子群，且分类精确到各个诱导特征的相等性，包括类型\(D_{4r+2}\)和\(B_3\)的额外模型。我们推导了相关的有限Gelfand对和交换子结论，并为额外的经典模型构造了典范Hecke结构。
英文摘要：
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.
