3D Bosons and W1+∞ algebra

Abstract

In this paper, we consider 3D Young diagrams with at most N layers in z-axis direction, which can be constructed by N 2D Young diagrams on slice z = j, j = 1, 2, · · · , N from the Yang-Baxter equation. Using 2D Bosons {aj,m, m ∈ ℤ} associated to 2D Young diagrams on the slice z = j, we constructed 3D Bosons. Then we show the 3D Boson representation of W1+∞ algebra, and give the method to calculate the Littlewood-Richardson rule for 3-Jack polynomials.