3D boson representation of affine Yangian of gl(1) and 3D cut-and-join operators

Abstract

In this paper, we construct the 3D Bosonic Fock space, which is isomorphic to the vector space of 3D Young diagrams as graded vector spaces. Then we use 3D Bosons to represent the generators of the affine Yangian of gl(1) and show that the generators ψj in the affine Yangian of gl(1) are the 3D cut-and-join operators.