Planar Harmonic Polynomials of Type B
Charles F. Dunkl
Abstract
The hyperoctahedral group is the Weyl group of type B and is associated with a two-parameter family of differential-difference operators Ti, 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 (T1)2+(T2)2 and by all Ti 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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