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Pseudo-differential equations, and the Bethe ansatz for the classical Lie algebras

Dorey, Patrick, Dunning, Clare, Masoero, Davide, Suzuki, Junji, Tateo, Roberto (2007) Pseudo-differential equations, and the Bethe ansatz for the classical Lie algebras. Nuclear Physics B, 772 (3). pp. 249-289. ISSN 0550-3213. (doi:10.1016/j.nuclphysb.2007.02.029)

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http://dx.doi.org/10.1016/j.nuclphysb.2007.02.029

Abstract

The correspondence between ordinary differential equations and Bethe ansatz equations for integrable lattice models in their continuum limits is generalised to vertex models related to classical simple Lie algebras. New families of pseudo-differential equations are proposed, and a link between specific generalised eigenvalue problems for these equations and the Bethe ansatz is deduced. The pseudo-differential operators resemble in form the Miura-transformed Lax operators studied in work on generalised KdV equations, classical W-algebras and, more recently, in the context of the geometric Langlands correspondence. Negative-dimension and boundary-condition dualities are also observed

Item Type: Article
DOI/Identification number: 10.1016/j.nuclphysb.2007.02.029
Uncontrolled keywords: CONFORMAL FIELD-THEORY; NONLINEAR INTEGRAL-EQUATIONS; SOLVABLE LATTICE MODELS; KAC-MOODY ALGEBRAS; FUNCTIONAL RELATIONS; STOKES MULTIPLIERS; DIFFERENTIAL-EQUATIONS; ANHARMONIC-OSCILLATORS; REPRESENTATION-THEORY; SCHRODINGER-EQUATION
Subjects: Q Science > QC Physics
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Applied Mathematics
Depositing User: Clare Dunning
Date Deposited: 19 Dec 2007 18:55 UTC
Last Modified: 28 May 2019 13:36 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/1419 (The current URI for this page, for reference purposes)
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