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We have constructed 3D Bosons. In this paper, we show the 3D Bosonic Fockspace, which is isomorphic to the vector space of 3D Young diagrams as gradedvector spaces. We use 3D Bosons to represent the generators of the affineYangian of ${\mathfrak{gl}}(1)$ and define the 3D cut-and-join operators. Thenwe discuss the 3D Boson representation of $W$-operators in matrix models.

3D Boson representation of affine Yangian of ${\mathfrak{gl}}(1)$ and 3D cut-and-join operators