SIGMA 4 (2008), 082, 9 pages      arXiv:0812.0063      https://doi.org/10.3842/SIGMA.2008.082
Contribution to the Special Issue on Dunkl Operators and Related Topics

Some Orthogonal Polynomials in Four Variables

Charles F. Dunkl
Department of Mathematics, University of Virginia, Charlottesville, VA 22904-4137, USA

Received October 14, 2008, in final form November 24, 2008; Published online November 29, 2008

Abstract
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.

Key words: nonsymmetric Jack polynomials.

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