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

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

2011-10-24

arxiv.org/abs/1110.5310v1

Mathematics

Quantum Algebra

Latex, 38 pages

Scientific paper

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.

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