Harmonic polynomials of type A
are polynomials annihilated by the Dunkl Laplacian associated to the symmetric group acting as a reflection group on
. The Dunkl operators are denoted by
, and the Laplacian
. This paper finds the homogeneous harmonic polynomials annihilated by all
. 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.
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