  In this work, we study quantum crystal melting in three space dimensions.
Using an equivalent description in terms of dimers in a hexagonal lattice, we
recast the crystal melting Hamiltonian as an occupancy problem in a Kagome
lattice. The Hilbert space is spanned by states labeled by plane partitions and
writing them as a product of interlaced integer partitions, we define a
fermion-boson duality for plane partitions. Finally, based upon the latter
result we conjecture that the growth operators for the quantum Hamiltonian can
be represented in terms of the affine Yangian ${\cal
Y}[\widehat{\mathfrak{gl}}(1)]$.
