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Intertwining Operator and h-Harmonics Associated With Reflection Groups

Published online by Cambridge University Press:  20 November 2018

Yuan Xu
Yuan Xu*
Affiliation:
Department of Mathematics University of Oregon Eugene, Oregon 97403-1222 U.S.A. e-mail: yuan@math.uoregon.edu
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Abstract

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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

33C5033C45h-harmonicsintertwining operatorreflection group
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 50 , Issue 1 , 01 February 1998 , pp. 193 - 209
Copyright
Copyright © Canadian Mathematical Society 1998

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