Some Orthogonal Polynomials in Four Variables

Details Some Orthogonal Polynomials in Four Variables Some Orthogonal Polynomials in Four Variables

2008-11-29

arxiv.org/abs/0812.0063v1

SIGMA 4 (2008), 082, 9 pages

Mathematics

Classical Analysis and ODEs

This is a contribution to the Special Issue on Dunkl Operators and Related Topics, published in SIGMA (Symmetry, Integrability

Scientific paper

10.3842/SIGMA.2008.082

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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