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arXiv · 0812.0063

Some Orthogonal Polynomials in Four Variables

Charles F. Dunkl
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Abstract

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.

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Charles F. Dunkl. 2008-11-29. Some Orthogonal Polynomials in Four Variables. https://doi.org/10.3842/sigma.2008.082

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