Charles F. Dunkl
Published 2008-11-29Version 1
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.
Comments: This is a contribution to the Special Issue on Dunkl Operators and Related Topics, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/
Journal: SIGMA 4 (2008), 082, 9 pages
On the norms and roots of orthogonal polynomials in the plane and $L^p$-optimal polynomials with respect to varying weights
Riemann-Hilbert Methods in the Theory of Orthogonal Polynomials
Normal matrix models, dbar-problem, and orthogonal polynomials on the complex plane
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