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

Dunning, C. and Dorey, P. and Masoero, D. and Suzuki, J. and Tateo, R. (2007) Pseudo-differential equations, and the Bethe ansatz for the classical Lie algebras. Nuclear Physics B, 772 (3). pp. 249-289. ISSN 0550-3213. (Full text available)

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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
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 > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science > Applied Mathematics
Depositing User: Stephen Holland
Date Deposited: 19 Dec 2007 18:55
Last Modified: 05 Sep 2011 23:23
Resource URI: http://kar.kent.ac.uk/id/eprint/1419 (The current URI for this page, for reference purposes)
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