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(38) Production(s) de CRAMPÉ N.
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Set-theoretical reflection equation: Classification of reflection maps 
Auteur(s): Caudrelier V., Crampé N., Zhang Q. C.
(Article) Publié:
Journal Of Physics A: Mathematical And Theoretical, vol. 46 p.095203 (2013)
Texte intégral en Openaccess : 
Ref HAL: hal-00789371_v1
Ref Arxiv: 1210.5107
DOI: 10.1088/1751-8113/46/9/095203
WoS: 000315154000011
Ref. & Cit.: NASA ADS
Exporter : BibTex | endNote
14 Citations
Résumé: The set-theoretical reflection equation and its solutions, the reflection maps, recently introduced by two of the authors, is presented in general and then applied in the context of quadrirational Yang-Baxter maps. We provide a method for constructing reflection maps and we obtain a classification of solutions associated to all the families of quadrirational Yang-Baxter maps that have been classified recently.
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Algebraic Bethe ansatz for open XXX model with triangular boundary matrices
Auteur(s): Belliard S., Crampé N., Ragoucy E.
(Article) Publié:
Letters In Mathematical Physics, vol. 103 p.493 (2013)
Texte intégral en Openaccess :
Ref HAL: hal-00733885_v1
Ref Arxiv: 1209.4269
DOI: 10.1007/s11005-012-0601-6
WoS: 000317675400002
Ref. & Cit.: NASA ADS
Exporter : BibTex | endNote
44 Citations
Résumé: We consider open XXX spins chain with two general boundary matrices submitted to one constraint, which is equivalent to the possibility to put the two matrices in a triangular form. We construct Bethe vectors from a generalized algebraic Bethe ansatz. As usual, the method also provides Bethe equations and transfer matrix eigenvalues.
Commentaires: 10 pges
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Coideal algebras from twisted Manin triples
Auteur(s): Crampé N., Belliard S.
(Article) Publié:
Journal Of Geometry And Physics, vol. 62 p.2009 (2012)
Texte intégral en Openaccess :
Ref HAL: hal-00670317_v1
Ref Arxiv: 1202.2312
DOI: 10.1016/j.geomphys.2012.05.008
WoS: 000307610700002
Ref. & Cit.: NASA ADS
Exporter : BibTex | endNote
17 Citations
Résumé: We propose a new approach to study coideal algebras. It is well-known that Manin triples (or equivalently Lie bi-algebra structures) are the requirement to deform Lie algebras and to obtain quantum groups. In this paper, introducing some particular automorphisms of Manin triples, we define new structures that we call Lie bi-ideal structures. A link with coisotropic subalgebras is explained. We show that their deformation provide coideal algebras. As examples, we recover from our general construction the twisted Yangians, the q-Onsager algebra and the augmented q-Onsager algebra. As an important by-product, we find a new presentation for the twisted Yangians.
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Matrix Coordinate Bethe Ansatz: Applications to XXZ and ASEP models
Auteur(s): Crampé N., Ragoucy E., Simon D.
(Article) Publié:
Journal Of Physics A: Mathematical And Theoretical, vol. 44 p.405003 (2011)
Texte intégral en Openaccess :
Ref HAL: hal-00603322_v1
Ref Arxiv: 1106.4712
DOI: 10.1088/1751-8113/44/40/405003
WoS: 000295840400004
Ref. & Cit.: NASA ADS
Exporter : BibTex | endNote
35 Citations
Résumé: We present the construction of the full set of eigenvectors of the open ASEP and XXZ models with special constraints on the boundaries. The method combines both recent constructions of coordinate Bethe Ansatz and the old method of matrix Ansatz specific to the ASEP. This "matrix coordinate Bethe Ansatz" can be viewed as a non-commutative coordinate Bethe Ansatz, the non-commutative part being related to the algebra appearing in the matrix Ansatz.
Commentaires: 18 pages.
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Generalized coordinate Bethe ansatz for non diagonal boundaries
Auteur(s): Crampé N., Ragoucy E.
(Article) Publié:
Nuclear Physics B, vol. 858 p.502 (2012)
Texte intégral en Openaccess :
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Eigenvectors of open XXZ and ASEP models for a class of non-diagonal boundary conditions
Auteur(s): Crampé N., Ragoucy Eric, Simon Damien
(Article) Publié:
Journal Of Statistical Mechanics: Theory And Experiment, vol. p.P11038 (2010)
Texte intégral en Openaccess :
Ref HAL: hal-00520424_v1
Ref Arxiv: 1009.4119
DOI: 10.1088/1742-5468/2010/11/P11038
WoS: 000286468600039
Ref. & Cit.: NASA ADS
Exporter : BibTex | endNote
39 Citations
Résumé: We present a generalization of the coordinate Bethe ansatz that allows us to solve integrable open XXZ and ASEP models with non-diagonal boundary matrices, provided their parameters obey some relations. These relations extend the ones already known in the literature in the context of algebraic or functional Bethe ansatz. The eigenvectors are represented as sums over cosets of the BC(n) Weyl group.
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Coordinate Bethe ansatz for spin s XXX model
Auteur(s): Crampé N., Ragoucy E., Alonzi L.
(Article) Publié:
Symmetry, Integrability And Geometry: Methods And Applications, vol. 7 p.006 (2011)
Texte intégral en Openaccess :
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