Characters of representations of the quantum toroidal algebra Open image in new window : Plane partitions with “stands”
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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 ⩽ j ⩽ n, which is the character of an irreducible representation of the quantum toroidal algebra Open image in new window , is obtained.
Key wordsplane partitions RSK algorithm representations of the Lie algebra
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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
- R. Stanley, Enumerative Combinatorics, vol. 2, Cambridge Univ. Press, Cambridge, 2001.Google Scholar