Quantum Integrable Model of an Arrangement of Hyperplanes

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2011
• ISSN: 1815-0659
• Main Author: Varchenko, A.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2011
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/146807
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Quantum Integrable Model of an Arrangement of Hyperplanes / A. Varchenko // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 29 назв. — англ.

The goal of this paper is to give a geometric construction of the Bethe algebra (of Hamiltonians) of a Gaudin model associated to a simple Lie algebra. More precisely, in this paper a quantum integrable model is assigned to a weighted arrangement of affine hyperplanes. We show (under certain assumpt...