Quantum toroidal $\mathfrak{gl}_1$ algebra : plane partitions
Quantum Algebra
2015-01-14 v1 Mathematical Physics
math.MP
Abstract
In 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.
Cite
@article{arxiv.1110.5310,
title = {Quantum toroidal $\mathfrak{gl}_1$ algebra : plane partitions},
author = {B. Feigin and M. Jimbo and T. Miwa and E. Mukhin},
journal= {arXiv preprint arXiv:1110.5310},
year = {2015}
}
Comments
Latex, 38 pages