Planar harmonic polynomials of type B

The hyperoctahedral group acting on R-N is the Weyl group of type B and is associated with a two-parameter family of differential-difference operators {T-i: 1 less than or equal to i less than or equal to N}. These operators are analogous to partial derivative operators. This paper finds all the pol ynomials h on R-N which are harmonic, Delta(B)h = 0 and annihilated by T-i for i > 2, where the Laplacian Delta(B) = Sigma(i=1)(N) T-i(2). They are gi ven explicitly in terms of a novel basis of polynomials, defined by generat ing functions. The harmonic polynomials can be used to find wavefunctions f or the quantum many-body spin Calogero model.