Quantum toroidal $\mathfrak{gl}_1$ algebra : plane partitions
  In third paper of the series we construct a large family of representations of the quantum toroidal $\gl_1$ algebra whose bases are parameterized by plane partitions with various boundary conditions and restrictions. We study the corresponding formal characters. As an application we obtain a Gelfand-Zetlin type basis for a class of irreducible lowest weight $\gl_\infty$-modules. 
B. Feigin, M. Jimbo, T. Miwa and E. Mukhin
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