English

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 \gl1\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\gl_\infty-modules.

Keywords

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

R2 v1 2026-06-21T19:24:53.131Z