Geodesic
The Quantum Toroidal Algebra $\widehat{\widehat{\mathfrak{gl}_1}}$: Calculation of Characters of Some Representations as Generating Functions of Plane Partitions
Funkcionalʹnyj analiz i ego priloženiâ, Tome 47 (2013) no. 1, pp. 62-76

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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 $K=q_1^mq_2^n$.
Mots-clés : plane partitions
Keywords: RSK algorithm, representations of the Lie algebra $\mathfrak{gl}(\infty)$. 
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     title = {The {Quantum} {Toroidal} {Algebra} $\widehat{\widehat{\mathfrak{gl}_1}}$: {Calculation} of {Characters} of {Some} {Representations} as {Generating} {Functions} of {Plane} {Partitions}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
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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. Funkcionalʹnyj analiz i ego priloženiâ, Tome 47 (2013) no. 1, pp. 62-76. http://geodesic.mathdoc.fr/item/FAA_2013_47_1_a5/