Quantum toroidal $\mathfrak{gl}_1$ algebra : plane partitions

Understand

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.