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PreprintCC0arXiv

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

  • Yifeng Zhang
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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 D4r+2 and B3. We derive the associated finite Gelfand-pair and commutant consequences, construct canonical Hecke structures for the additional classical models.

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Cite

BibTeXRIS
BibTeX
@misc{zhang2026quasiparabolic,
  title = {{Quasiparabolic Gelfand models for finite irreducible Coxeter groups and their canonical Hecke structures}},
  author = {Yifeng Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.15235},
  eprint = {2609.15235},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.15235},
  note = {CC0},
}
RIS
TY  - UNPB
TI  - Quasiparabolic Gelfand models for finite irreducible Coxeter groups and their canonical Hecke structures
AU  - Yifeng Zhang
PY  - 2026
DA  - 2026/09/16
PB  - arXiv
DO  - 10.48550/arxiv.2609.15235
UR  - https://arxiv.org/abs/2609.15235
AB  - 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.
ER  -