Generalization of the Uq(gl(N)) algebra and staggered models

D. Arnaudon; A. Sedrakyan; T. Sedrakyan; P. Sorba

doi:10.1023/A:1014504526934

Generalization of the Uq(gl(N)) algebra and staggered models

D. Arnaudon, A. Sedrakyan, T. Sedrakyan, P. Sorba

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5 Scopus citations

Abstract

We develop a technique for the construction of integrable models with a ℤ₂ grading of both the auxiliary (chain) and quantum (time) spaces. These models have a staggered disposition of the anisotropy parameter. The corresponding Yang-Baxter equations are written down and their solution for the gl(N) case is found. We analyze in details the N = 2 case and find the corresponding quantum group behind this solution. It can be regarded as the quantum group U_qB(gl(2)), with a matrix deformation parameter qB such that (qB)² = q². The symmetry behind these models can also be interpreted as the tensor product of the (-1)-Weyl algebra by an extension of U_q(gl(N)) with a Cartan generator related to deformation parameter -1.

Original language	English (US)
Pages (from-to)	209-222
Number of pages	14
Journal	Letters in Mathematical Physics
Volume	58
Issue number	3
DOIs	https://doi.org/10.1023/A:1014504526934
State	Published - Dec 2001
Externally published	Yes

Bibliographical note

Funding Information:
The authors, A.S. and T.S., acknowledge the LAPTH for hospitality, where this work was carried out. T.S. also acknowledges INTAS grant 99-1459 and A.S acknowledges the partial ¢nancial support of grant 00-390.

Keywords

Bethe Ansatz
Integrable models
Ladder models
Quantum groups
Staggered parameters

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title = "Generalization of the Uq(gl(N)) algebra and staggered models",

abstract = "We develop a technique for the construction of integrable models with a ℤ2 grading of both the auxiliary (chain) and quantum (time) spaces. These models have a staggered disposition of the anisotropy parameter. The corresponding Yang-Baxter equations are written down and their solution for the gl(N) case is found. We analyze in details the N = 2 case and find the corresponding quantum group behind this solution. It can be regarded as the quantum group UqB(gl(2)), with a matrix deformation parameter qB such that (qB)2 = q2. The symmetry behind these models can also be interpreted as the tensor product of the (-1)-Weyl algebra by an extension of Uq(gl(N)) with a Cartan generator related to deformation parameter -1.",

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author = "D. Arnaudon and A. Sedrakyan and T. Sedrakyan and P. Sorba",

note = "Funding Information: The authors, A.S. and T.S., acknowledge the LAPTH for hospitality, where this work was carried out. T.S. also acknowledges INTAS grant 99-1459 and A.S acknowledges the partial ¢nancial support of grant 00-390.",

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AU - Sedrakyan, A.

AU - Sedrakyan, T.

AU - Sorba, P.

N1 - Funding Information: The authors, A.S. and T.S., acknowledge the LAPTH for hospitality, where this work was carried out. T.S. also acknowledges INTAS grant 99-1459 and A.S acknowledges the partial ¢nancial support of grant 00-390.

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N2 - We develop a technique for the construction of integrable models with a ℤ2 grading of both the auxiliary (chain) and quantum (time) spaces. These models have a staggered disposition of the anisotropy parameter. The corresponding Yang-Baxter equations are written down and their solution for the gl(N) case is found. We analyze in details the N = 2 case and find the corresponding quantum group behind this solution. It can be regarded as the quantum group UqB(gl(2)), with a matrix deformation parameter qB such that (qB)2 = q2. The symmetry behind these models can also be interpreted as the tensor product of the (-1)-Weyl algebra by an extension of Uq(gl(N)) with a Cartan generator related to deformation parameter -1.

AB - We develop a technique for the construction of integrable models with a ℤ2 grading of both the auxiliary (chain) and quantum (time) spaces. These models have a staggered disposition of the anisotropy parameter. The corresponding Yang-Baxter equations are written down and their solution for the gl(N) case is found. We analyze in details the N = 2 case and find the corresponding quantum group behind this solution. It can be regarded as the quantum group UqB(gl(2)), with a matrix deformation parameter qB such that (qB)2 = q2. The symmetry behind these models can also be interpreted as the tensor product of the (-1)-Weyl algebra by an extension of Uq(gl(N)) with a Cartan generator related to deformation parameter -1.

KW - Bethe Ansatz

KW - Integrable models

KW - Ladder models

KW - Quantum groups

KW - Staggered parameters

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EP - 222

JO - Letters in Mathematical Physics

JF - Letters in Mathematical Physics

IS - 3

ER -

Generalization of the Uq(gl(N)) algebra and staggered models

Abstract

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Keywords

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