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Funktsional. Anal. i Prilozhen., 2013, Volume 47, Issue 1, Pages 62–76 (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

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 $\mathfrak{gl}(\infty)$

DOI: https://doi.org/10.4213/faa3097

Full text: PDF file (226 kB)
References: PDF file   HTML file

English version:
Functional Analysis and Its Applications, 2013, 47:1, 50–61

Bibliographic databases:

UDC: 519.116+517.986.5
Received: 26.07.2012

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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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. G. S. Mutafyan, B. L. Feigin, “Characters of Representations of the Quantum Toroidal Algebra $\widehat{\widehat{\mathfrak{gl}_1}}$: Plane Partitions with “Stands””, Funct. Anal. Appl., 48:1 (2014), 36–48  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. Molev A.I. Mukhin E.E., “Invariants of the Vacuum Module Associated With the Lie Superalgebra Gl(1 Vertical Bar 1)”, J. Phys. A-Math. Theor., 48:31, SI (2015), 314001  crossref  mathscinet  zmath  isi  elib  scopus
    3. M. Bershtein, B. Feigin, G. Merzon, “Plane partitions with a “pit”: generating functions and representation theory”, Sel. Math.-New Ser., 24:1, SI (2018), 21–62  crossref  mathscinet  zmath  isi  scopus
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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