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Intertwining Operator and h-Harmonics Associated With Reflection Groups

Published online by Cambridge University Press:  20 November 2018

Yuan Xu*
Affiliation:
Department of Mathematics University of Oregon Eugene, Oregon 97403-1222 U.S.A. e-mail: [email protected]
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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.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1998

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