Quantum toroidal gl1-algebra: Plane partitions

Abstract

In this, the third paper of the series, we construct a large family of representations of the quantum toroidal gl1-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-modules. © 2012 by Kyoto University.