Pseudo-differential equations,and the Bethe ansatz for the classical Lie algebras |
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Authors: | Patrick Dorey Clare Dunning Davide Masoero Junji Suzuki Roberto Tateo |
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Institution: | 1. Department of Mathematical Sciences, University of Durham, Durham DH1 3LE, United Kingdom;2. IMSAS, University of Kent, Canterbury, UK CT2 7NF, United Kingdom;3. SISSA, via Beirut 2-4, 34014 Trieste, Italy;4. Department of Physics, Shizuoka University, Ohya 836, SURUGA, Shizuoka, Japan;5. Dipartimento di Fisica Teorica and INFN, Università di Torino, Via P. Giuria 1, 10125 Torino, Italy |
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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. |
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Keywords: | 03 65 Ge 11 15 Tk 11 25 Hf 11 55 Ds |
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