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Planar Harmonic and Monogenic Polynomials of Type A

Department of Mathematics, University of Virginia, P.O. Box 400137, Charlottesville, VA 22904-4137, USA
Academic Editor: Hari M. Srivastava
Symmetry 2016, 8(10), 108; https://doi.org/10.3390/sym8100108
Received: 8 September 2016 / Revised: 12 October 2016 / Accepted: 14 October 2016 / Published: 21 October 2016
(This article belongs to the Special Issue Symmetry in Orthogonal Polynomials)
Harmonic polynomials of type A are polynomials annihilated by the Dunkl Laplacian associated to the symmetric group acting as a reflection group on R N . The Dunkl operators are denoted by T j for 1 j N , and the Laplacian Δ κ = j = 1 N T j 2 . This paper finds the homogeneous harmonic polynomials annihilated by all T j for j > 2 . The structure constants with respect to the Gaussian and sphere inner products are computed. These harmonic polynomials are used to produce monogenic polynomials, those annihilated by a Dirac-type operator. View Full-Text
Keywords: Dunkl operators; symmetric group; harmonic polynomials Dunkl operators; symmetric group; harmonic polynomials
MDPI and ACS Style

Dunkl, C.F. Planar Harmonic and Monogenic Polynomials of Type A. Symmetry 2016, 8, 108.

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