3D bosons, 3-Jack polynomials and affine Yangian of gl(1)

3D (3 dimensional) Young diagrams are a generalization of 2D Young diagrams. In this paper, We consider 3D Bosons and 3-Jack polynomials. We associate three parameters h(1), h(2), h(3) to y, x, z-axis respectively. 3-Jack polynomials are polynomials of P-n,P-j, n = j with coefficients in DOUBLE-STRUCK CAPITAL C(h(1), h(2), h(3)), which are the generalization of Schur functions and Jack polynomials to 3D case. Similar to Schur functions, 3-Jack polynomials can also be determined by the vertex operators and the Pieri formulas.