In this, the third paper of the series, we construct a large family of representations of the quantum toroidal -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 -modules.
"Quantum toroidal -algebra: Plane partitions." Kyoto J. Math. 52 (3) 621 - 659, Fall 2012. https://doi.org/10.1215/21562261-1625217