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Planar Harmonic Polynomials of Type B

Charles F. Dunkl
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Abstract

The hyperoctahedral group is the Weyl group of type B and is associated with a two-parameter family of differential-difference operators T_i, i=1,..,N (the dimension of the underlying Euclidean space). These operators are analogous to partial derivative operators. This paper finds all the polynomials in N variables which are annihilated by the sum of the squares (T_1)^2+(T_2)^2 and by all T_i for i>2 (harmonic). They are given explicitly in terms of a novel basis of polynomials, defined by generating functions. The harmonic polynomials can be used to find wave functions for the quantum many-body spin Calogero model.

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Charles F. Dunkl. 1999-06-07. Planar Harmonic Polynomials of Type B. https://doi.org/10.1088/0305-4470%2F32%2F46%2F308

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