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This article is cited in 19 scientific papers (total in 19 papers)
Quantum Integrable Model of an Arrangement of Hyperplanes
Alexander Varchenko Department of Mathematics, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599-3250, USA
Abstract:
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.
Keywords:
Gaudin model; arrangement of hyperplanes.
Received: July 19, 2010; in final form March 19, 2011; Published online March 28, 2011
Citation:
Alexander Varchenko, “Quantum Integrable Model of an Arrangement of Hyperplanes”, SIGMA, 7 (2011), 032, 55 pp.
Linking options:
https://www.mathnet.ru/eng/sigma590 https://www.mathnet.ru/eng/sigma/v7/p32
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Abstract page: | 267 | Full-text PDF : | 63 | References: | 38 |
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