Manin Matrices, Quantum Elliptic Commutative Families and Characteristic Polynomial of Elliptic Gaudin Model

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2009
• ISSN: 1815-0659
• Main Authors: Rubtsov, V., Silantyev, A., Talalaev, D.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2009
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/149089
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Manin Matrices, Quantum Elliptic Commutative Families and Characteristic Polynomial of Elliptic Gaudin Model / V. Rubtsov, A. Silantyev, D. Talalaev // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 24 назв. — англ.

In this paper we construct the quantum spectral curve for the quantum dynamical elliptic gln Gaudin model. We realize it considering a commutative family corresponding to the Felder's elliptic quantum group Eτ,h(gln) and taking the appropriate limit. The approach of Manin matrices here suits we...