The quantum toroidal algebra gl1: Calculation of characters of some representations as generating functions of plane partitions

G. S. Mutafyan; B. L. Feigin

doi:10.1007/s10688-013-0006-z

The quantum toroidal algebra gl₁: Calculation of characters of some representations as generating functions of plane partitions

G. S. Mutafyan
, B. L. Feigin

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

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 gl₁ in the case K = q₁^mq₂ⁿ.

Original language	English
Pages (from-to)	50-61
Number of pages	12
Journal	Functional Analysis and its Applications
Volume	47
Issue number	1
DOIs	https://doi.org/10.1007/s10688-013-0006-z
State	Published - Mar 2013
Externally published	Yes

Keywords

RSK algorithm
plane partitions
representations of the Lie algebra gl(∞)

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10.1007/s10688-013-0006-z

Cite this

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title = "The quantum toroidal algebra gl1: Calculation of characters of some representations as generating functions of plane partitions",

abstract = "The generating function of plane partitions \{ai,j\} subject to the constraint am,n = 0 is expressed and calculated as the character of an irreducible representation of the quantum toroidal algebra gl1 in the case K = q1mq2n.",

keywords = "RSK algorithm, plane partitions, representations of the Lie algebra gl(∞)",

author = "Mutafyan, \{G. S.\} and Feigin, \{B. L.\}",

year = "2013",

month = mar,

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AB - The generating function of plane partitions {ai,j} subject to the constraint am,n = 0 is expressed and calculated as the character of an irreducible representation of the quantum toroidal algebra gl1 in the case K = q1mq2n.

KW - RSK algorithm

KW - plane partitions

KW - representations of the Lie algebra gl(∞)

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The quantum toroidal algebra gl₁: Calculation of characters of some representations as generating functions of plane partitions

Abstract

Keywords

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Квантовая тороидальная алгебра ˆ ˆ g l 1 : вычисление характеров некоторых представлений как производящих функций плоских разбиений

Cite this

The quantum toroidal algebra gl1: Calculation of characters of some representations as generating functions of plane partitions

Abstract

Keywords

Access to Document

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Related research output

Квантовая тороидальная алгебра ˆ ˆ g l 1 : вычисление характеров некоторых представлений как производящих функций плоских разбиений

Cite this

The quantum toroidal algebra gl₁: Calculation of characters of some representations as generating functions of plane partitions