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Funktsional'nyi Analiz i ego Prilozheniya, 2013, Volume 47, Issue 1, Pages 62–76
DOI: https://doi.org/10.4213/faa3097 (Mi faa3097) 		 
This article is cited in 3 scientific papers (total in 3 papers)

The Quantum Toroidal Algebra $\widehat{\widehat{\mathfrak{gl}_1}}$: Calculation of Characters of Some Representations as Generating Functions of Plane Partitions

G. S. Mutafyana, B. L. Feiginba

a National Research University "Higher School of Economics"
b L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences
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DOI: https://doi.org/10.4213/faa3097
Abstract: The generating function of plane partitions $\{a_{i,j}\}$ subject to the constraint $a_{m,n}=0$ is expressed and calculated as the character of an irreducible representation of the quantum toroidal algebra $\widehat{\widehat{\mathfrak{gl}}}_1$ in the case $K=q_1^mq_2^n$.
Keywords: plane partitions, RSK algorithm, representations of the Lie algebra $\mathfrak{gl}(\infty)$.
Received: 26.07.2012
English version:
Functional Analysis and Its Applications, 2013, Volume 47, Issue 1, Pages 50–61
DOI: https://doi.org/10.1007/s10688-013-0006-z
Bibliographic databases:
Document Type: Article
UDC: 519.116+517.986.5
Language: Russian
Citation: G. S. Mutafyan, B. L. Feigin, “The Quantum Toroidal Algebra $\widehat{\widehat{\mathfrak{gl}_1}}$: Calculation of Characters of Some Representations as Generating Functions of Plane Partitions”, Funktsional. Anal. i Prilozhen., 47:1 (2013), 62–76; Funct. Anal. Appl., 47:1 (2013), 50–61
Citation in format AMSBIB
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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