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arXiv · 1110.5310

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

B. Feigin·M. Jimbo·T. Miwa·E. Mukhin
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Abstract

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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B. Feigin, M. Jimbo, T. Miwa, E. Mukhin. 2011-10-24. Quantum toroidal $\mathfrak{gl}_1$ algebra : plane partitions. https://doi.org/10.1215/21562261-1625217

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