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Funktsional. Anal. i Prilozhen., 2014, Volume 48, Issue 1, Pages 46–60 (Mi faa3136)  

This article is cited in 2 scientific papers (total in 2 papers)

Characters of Representations of the Quantum Toroidal Algebra $\widehat{\widehat{\mathfrak{gl}_1}}$: Plane Partitions with “Stands”

G. S. Mutafyana, B. L. Feiginab

a National Research University "Higher School of Economics", Moscow
b L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences

Abstract: An expression for the generating function of plane partitions $a_{i,j}$ subject to the constraints $a_{m,n}=0$ and $a_{i,j}\ge k_j$, $1\le j\le n$, which is the character of an irreducible representation of the quantum toroidal algebra $\widehat{\widehat{\mathfrak{gl}_1}}$, is obtained.

Keywords: plane partitions, RSK algorithm, representations of the Lie algebra

DOI: https://doi.org/10.4213/faa3136

Full text: PDF file (249 kB)
References: PDF file   HTML file

English version:
Functional Analysis and Its Applications, 2014, 48:1, 36–48

Bibliographic databases:

UDC: 519.116+517.986.5
Received: 17.07.2013

Citation: G. S. Mutafyan, B. L. Feigin, “Characters of Representations of the Quantum Toroidal Algebra $\widehat{\widehat{\mathfrak{gl}_1}}$: Plane Partitions with “Stands””, Funktsional. Anal. i Prilozhen., 48:1 (2014), 46–60; Funct. Anal. Appl., 48:1 (2014), 36–48

Citation in format AMSBIB
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\pages 46--60
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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. Anatol N. Kirillov, “On Some Quadratic Algebras I $\frac{1}{2}$: Combinatorics of Dunkl and Gaudin Elements, Schubert, Grothendieck, Fuss–Catalan, Universal Tutte and Reduced Polynomials”, SIGMA, 12 (2016), 002, 172 pp.  mathnet  crossref
    2. 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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