Bochner-Martinelli Formula for Higher Spin Operators of Several R^(6) Variables

The higher spin operator of several R^(6)variables is an analogue of the■-operator in theory of several complex variables.The higher spin representation of so6(C)is⊙^(k)C_(4)and the higher spin operator D_(k) acts on⊙^(k)C_(4)-valued functions.In this paper,the authors establish the Bochner-Martinelli formula for higher spin operator Dk of several R^(6)variables.The embedding of R^(6n) into the space of complex 4n×4 matrices allows them to use two-component notation,which makes the spinor calculus on R^(6n)more concrete and explicit.A function annihilated by D_(k ) is called k-monogenic.They give the Penrose integral formula over R^(6n) and construct many k-monogenic polynomials.