Abstract
The symmetric group on 4 letters has the reflection group D3 as an isomor- phic 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 par- ticles on the line.
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