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## Quantum toroidal gl(1)-algebra: Plane partitions

Kyoto Journal of Mathematics. 2012. Vol. 52. No. 3. P. 621-659.
Feigin B. L., Jimbo M., Miwa T., Mukhin E.

In this, the 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(infinity)-modules.