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Some Orthogonal Polynomials in Four Variables
Symmetry, integrability and geometry: methods and applications, Tome 4 (2008) Cet article a éte moissonné depuis la source Math-Net.Ru

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The symmetric group on 4 letters has the reflection group $D_3$ as an isomorphic image. This fact follows from the coincidence of the root systems $A_3$ and $D_3$. 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.
Keywords: nonsymmetric Jack polynomials. 
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Charles F. Dunkl. Some Orthogonal Polynomials in Four Variables. Symmetry, integrability and geometry: methods and applications, Tome 4 (2008). http://geodesic.mathdoc.fr/item/SIGMA_2008_4_a81/

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