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 \(\widehat {\widehat {\mathfrak{g}{\mathfrak{l}_1}}}\) in the case K = q m1 q n2 .
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B. Feigin, M. Jimbo, T. Miwa, and E. Mukhin, “Quantum toroidal gl1 algebra: plane partitions,” Kyoto J. Math., 52:3, 621–659; http://arxiv.org/abs/1110.5310v1.
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Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 47, No. 1, pp. 62–76, 2013
Original Russian Text Copyright © by G. S. Mutafyan and B. L. Feigin
The work of B. L. Feigin was supported by RFBR grants nos. 12-01-00836-a and 12-01-00944-a and by Russian-French grant no. 11-01-93105-NTsNIL-a.
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Mutafyan, G.S., Feigin, B.L. The quantum toroidal algebra \(\widehat {\widehat {\mathfrak{g}{\mathfrak{l}_1}}}\): Calculation of characters of some representations as generating functions of plane partitions. Funct Anal Its Appl 47, 50–61 (2013). https://doi.org/10.1007/s10688-013-0006-z
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DOI: https://doi.org/10.1007/s10688-013-0006-z