Some Orthogonal Polynomials in Four Variables

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2008
• Main Author: Dunkl, C.F.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2008
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/149009
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Some Orthogonal Polynomials in Four Variables / C.F. Dunkl // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 5 назв. — англ.

The symmetric group on 4 letters has the reflection group D₃ as an isomorphic image. This fact follows from the coincidence of the root systems A₃ and D₃. The isomorphism is used to construct an orthogonal basis of polynomials of 4 variables with 2 parameters. There is an associated quantum Calogero...