Quantum toroidal \mathfrakgl₁ algebra : plane partitions

2011/10/24 by B. Feigin, M. Jimbo, T. Miwa +1 · 1 citation
Mathematics · Physics and Astronomy · #math-ph #math.MP #math.QA

paper · pdf · doi:10.1215/21562261-1625217

published as Kyoto J. Math. 52, no. 3 (2012), 621-659 · Latex, 38 pages

arxiv created 2011/10/24 · arxiv updated 2015/01/14

Abstract

In 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.

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• Free field realization of the quantum toroidal algebra of \mathfrakgl₁ with general levels