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Functional Analysis and Its Applications

, Volume 48, Issue 1, pp 36–48 | Cite as

Characters of representations of the quantum toroidal algebra Open image in new window : Plane partitions with “stands”

  • G. S. MutafyanEmail author
  • B. L. Feigin
Article
  • 84 Downloads

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 k j , 1 ⩽ jn, which is the character of an irreducible representation of the quantum toroidal algebra Open image in new window , is obtained.

Key words

plane partitions RSK algorithm representations of the Lie algebra 

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References

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    G. S. Mutafyan and B. L. Feigin, “The quantum toroidal algebra Open image in new window: Calculation of characters of some representations as generating functions of plane partitions,” Funkts. Anal. i Ego Prilozh., 47:1 (2013), 62–76; English translation: Funct. Anal. and Its Appl., 47: 1 (2013), 50–61.CrossRefMathSciNetGoogle Scholar
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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Higher School of Economics, L. D. Landau Institute of Theoretical PhysicsRussian Academy of SciencesChernogolovkaRussia

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