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# Intertwining operator and $h$-harmonics associated with reflection groups

Published:1998-02-01
Printed: Feb 1998
• Yuan Xu
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## Abstract

We study the intertwining operator and $h$-harmonics in Dunkl's theory on $h$-harmonics associated with reflection groups. Based on a biorthogonality between the ordinary harmonics and the action of the intertwining operator $V$ on the harmonics, the main result provides a method to compute the action of the intertwining operator $V$ on polynomials and to construct an orthonormal basis for the space of $h$-harmonics.
 Keywords: $h$-harmonics, intertwining operator, reflection group
 MSC Classifications: 33C50 - Orthogonal polynomials and functions in several variables expressible in terms of special functions in one variable 33C45 - Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) [See also 42C05 for general orthogonal polynomials and functions]