Some Spherical Function Values for Hook Tableaux Isotypes and Young Subgroups

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2025
• ISSN: 1815-0659
• Main Author: Dunkl, Charles F.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2025
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/213523
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Some Spherical Function Values for Hook Tableaux Isotypes and Young Subgroups. Charles F. Dunkl. SIGMA 21 (2025), 053, 17 pages

A Young subgroup of the symmetric group N, the permutation group of {1, 2, …, }, is generated by a subset of the adjacent transpositions {(, +1)∣1 ≤ < }. Such a group is realized as the stabilizer ₙ of a monomial λ (=λ¹₁λ²₂ ⋯ λᴺN) with λ = (ⁿ¹₁, ⁿ²₂, …, ⁿᵖₚ) (meaning ⱼ is repeated ⱼ times, 1...