Quantum Integrable Model of an Arrangement of Hyperplanes
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Quantum Integrable Model of an Arrangement of Hyperplanes
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| Creator |
Varchenko, A.
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| Description |
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 assumptions) that the algebra of Hamiltonians of the model is isomorphic to the algebra of functions on the critical set of the corresponding master function. For a discriminantal arrangement we show (under certain assumptions) that the symmetric part of the algebra of Hamiltonians is isomorphic to the Bethe algebra of the corresponding Gaudin model. It is expected that this correspondence holds in general (without the assumptions). As a byproduct of constructions we show that in a Gaudin model (associated to an arbitrary simple Lie algebra), the Bethe vector, corresponding to an isolated critical point of the master function, is nonzero.
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| Date |
2019-02-11T15:45:50Z
2019-02-11T15:45:50Z 2011 |
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| Type |
Article
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| Identifier |
Quantum Integrable Model of an Arrangement of Hyperplanes / A. Varchenko // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 29 назв. — англ.
1815-0659 2010 Mathematics Subject Classification: 82B23; 32S22; 17B81; 81R12 DOI:10.3842/SIGMA.2011.032 http://dspace.nbuv.gov.ua/handle/123456789/146807 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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