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Generating Series for Nested Bethe Vectors
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2008, том 4
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Generating Series for Nested Bethe Vectors
Інший ID:
2000 Mathematics Subject Classification: 17B37; 81R50
Посилання:
Generating Series for Nested Bethe Vectors / S. Khoroshkin, S. Pakuliak // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 18 назв. — англ.
Підтримка:
This paper is a contribution to the Special Issue on Kac–Moody Algebras and Applications. The main idea to use generating series for the description of the hierarchical Bethe ansatz appeared during authors visit to Max-Planck Institute f¨ur Mathematik, Bonn, in January, 2008. Authors acknowledge this scientific center for the hospitality and stimulating scientific atmosphere.This work was partially done when the second author (S.P.) visited Laboratoire d’Annecy-LeVieux de Physique Th´eorique in 2006 and 2007. These visits were possible due to the financial support of the CNRS-Russia exchange program on mathematical physics. He thanks LAPTH for the hospitality and stimulating scientific atmosphere. Authors are grateful to Luc Frappat and Eric Ragoucy for many helpful discussions. The authors were supported in part by RFBR grant 08-01-00392 and grant for the support of scientific schools NSh-3036.2008.2. The first author was also supported by the Atomic Energy Agency of the Russian Federation, and by the ANR grant 05-BLAN-0029-01. The second author was also supported in part by RFBR-CNRS grant 07-02-92166-CNRS.
Дата:
2008
Переглядів:
499
Завантажень:
233
Анотація:
We reformulate nested relations between off-shell Uq(^glN) Bethe vectors as a certain equation on generating series of strings of the composed Uq(^glN) currents. Using inversion of the generating series we find a new type of hierarchical relations between universal off-shell Bethe vectors, useful for a derivation of Bethe equation. As an example of application, we use these relations for a derivation of analytical Bethe ansatz equations [Arnaudon D. et al., Ann. Henri Poincaré 7 (2006), 1217-1268, math-ph/0512037] for the parameters of universal Bethe vectors of the algebra Uq(^gl2).
