Quantum loop algebras and l-root operators

Charles Young

doi:10.1007/s00031-015-9339-4

Quantum loop algebras and l-root operators

Charles Young

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Abstract

Let g be a simple Lie algebra and q transcendental. We consider the category C_P of finite-dimensional representations of the quantum loop algebra Uq(Lg) in which the poles of all l-weights belong to specified finite sets P. Given the data (g,q,P), we define an algebra A whose raising/lowering operators are constructed to act with definite l-weight (unlike those of Uq(Lg) itself). It is shown that there is a homomorphism Uq(Lg) -> A such that every representation V in C_P is the pull-back of a representation of A.

Original language	English
Pages (from-to)	1195-1226
Number of pages	32
Journal	Transformation Groups
Volume	20
Issue number	4
Early online date	18 Sept 2015
DOIs	https://doi.org/10.1007/s00031-015-9339-4
Publication status	Published - 1 Dec 2015

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10.1007/s00031-015-9339-4

Accepted ManuscriptAccepted author manuscript, 904 KBLicence: CC BY

http://arxiv.org/abs/1206.6657

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title = "Quantum loop algebras and l-root operators",

abstract = "Let g be a simple Lie algebra and q transcendental. We consider the category C_P of finite-dimensional representations of the quantum loop algebra Uq(Lg) in which the poles of all l-weights belong to specified finite sets P. Given the data (g,q,P), we define an algebra A whose raising/lowering operators are constructed to act with definite l-weight (unlike those of Uq(Lg) itself). It is shown that there is a homomorphism Uq(Lg) -> A such that every representation V in C_P is the pull-back of a representation of A.",

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N2 - Let g be a simple Lie algebra and q transcendental. We consider the category C_P of finite-dimensional representations of the quantum loop algebra Uq(Lg) in which the poles of all l-weights belong to specified finite sets P. Given the data (g,q,P), we define an algebra A whose raising/lowering operators are constructed to act with definite l-weight (unlike those of Uq(Lg) itself). It is shown that there is a homomorphism Uq(Lg) -> A such that every representation V in C_P is the pull-back of a representation of A.

AB - Let g be a simple Lie algebra and q transcendental. We consider the category C_P of finite-dimensional representations of the quantum loop algebra Uq(Lg) in which the poles of all l-weights belong to specified finite sets P. Given the data (g,q,P), we define an algebra A whose raising/lowering operators are constructed to act with definite l-weight (unlike those of Uq(Lg) itself). It is shown that there is a homomorphism Uq(Lg) -> A such that every representation V in C_P is the pull-back of a representation of A.

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DO - 10.1007/s00031-015-9339-4

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VL - 20

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EP - 1226

JO - Transformation Groups

JF - Transformation Groups

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ER -

Quantum loop algebras and l-root operators

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