On irreducibility of tensor products of Yangian modules

Maxim Nazarov; Vitaly Tarasov

doi:10.1155/S1073792898000129

On irreducibility of tensor products of Yangian modules

Maxim Nazarov, Vitaly Tarasov

Mathematics

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

Abstract

We study the tensor product $V$ of any number of "elementary" irreducible modules over the Yangian of the general linear Lie algebra. An elementary module is determined by a skew Young diagram and by a complex parameter, and contains a vector called singular. We give sufficient conditions for cyclicity in $V$ of the tensor product of these singular vectors. By using this result, we give an irreducibility criterion for $V$ when each of the skew Young diagrams determining the tensor factors has rectangular shape.

Original language	English
Pages (from-to)	125-150
Number of pages	26
Journal	International Mathematics Research Notices
Volume	1998
Issue number	3
DOIs	https://doi.org/10.1155/S1073792898000129
Publication status	Published - 1998

Keywords

MODEL

Access to Document

10.1155/S1073792898000129

http://arxiv.org/abs/q-alg/9712004

Cite this

@article{bd6e20a29c154456baeea0a0fa13442b,

title = "On irreducibility of tensor products of Yangian modules",

abstract = "We study the tensor product $V$ of any number of {"}elementary{"} irreducible modules over the Yangian of the general linear Lie algebra. An elementary module is determined by a skew Young diagram and by a complex parameter, and contains a vector called singular. We give sufficient conditions for cyclicity in $V$ of the tensor product of these singular vectors. By using this result, we give an irreducibility criterion for $V$ when each of the skew Young diagrams determining the tensor factors has rectangular shape. ",

keywords = "MODEL",

author = "Maxim Nazarov and Vitaly Tarasov",

year = "1998",

doi = "10.1155/S1073792898000129",

language = "English",

volume = "1998",

pages = "125--150",

journal = "International Mathematics Research Notices",

issn = "1687-0247",

publisher = "Oxford University Press",

number = "3",

}

TY - JOUR

T1 - On irreducibility of tensor products of Yangian modules

AU - Nazarov, Maxim

AU - Tarasov, Vitaly

PY - 1998

Y1 - 1998

N2 - We study the tensor product $V$ of any number of "elementary" irreducible modules over the Yangian of the general linear Lie algebra. An elementary module is determined by a skew Young diagram and by a complex parameter, and contains a vector called singular. We give sufficient conditions for cyclicity in $V$ of the tensor product of these singular vectors. By using this result, we give an irreducibility criterion for $V$ when each of the skew Young diagrams determining the tensor factors has rectangular shape.

AB - We study the tensor product $V$ of any number of "elementary" irreducible modules over the Yangian of the general linear Lie algebra. An elementary module is determined by a skew Young diagram and by a complex parameter, and contains a vector called singular. We give sufficient conditions for cyclicity in $V$ of the tensor product of these singular vectors. By using this result, we give an irreducibility criterion for $V$ when each of the skew Young diagrams determining the tensor factors has rectangular shape.

KW - MODEL

U2 - 10.1155/S1073792898000129

DO - 10.1155/S1073792898000129

M3 - Article

SN - 1687-0247

VL - 1998

SP - 125

EP - 150

JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

IS - 3

ER -