Some Orthogonal Polynomials in Four Variables - Dunkl, C.F. (Symmetry, Integrability and Geometry: Methods and Applications, 2008)
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-Sutherland model of 4 identical particles on the line.