Bethe Ansatz and the spectral theory of affine Lie algebra–valued connections II: the non simply–laced case

Masoero, D., Raimondo, A. and Valeri, D. (2017) Bethe Ansatz and the spectral theory of affine Lie algebra–valued connections II: the non simply–laced case. Communications in Mathematical Physics, 349(3), pp. 1063-1105. (doi: 10.1007/s00220-016-2744-2)

Abstract

We assess the ODE/IM correspondence for the quantum g-KdV model, for a non-simply laced Lie algebra g. This is done by studying a meromorphic connection with values in the Langlands dual algebra of the affine Lie algebra g(1), and constructing the relevant Ψ-system among subdominant solutions. We then use the Ψ-system to prove that the generalized spectral determinants satisfy the Bethe Ansatz equations of the quantum g-KdV model. We also consider generalized Airy functions for twisted Kac–Moody algebras and we construct new explicit solutions to the Bethe Ansatz equations. The paper is a continuation of our previous work on the ODE/IM correspondence for simply-laced Lie algebras.

• Item Type: Articles
• Additional Information: The authors were partially supported by the INdAM-GNFM “Progetto Giovani 2014”. DM is supported by the FCT scholarship, number SFRH/BPD/75908/2011. AR is supported by the FCT project “Incentivo/MAT/ UI0208/2014”. DV is supported by an NSFC “Research Fund for International Young Scientists” Grant. We thank Edward Frenkel for useful discussions.
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Valeri, Dr Daniele
• Authors: Masoero, D., Raimondo, A., and Valeri, D.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Communications in Mathematical Physics
• Publisher: Springer
• ISSN: 0010-3616
• ISSN (Online): 1432-0916
• Published Online: 17 September 2016
• Copyright Holders: Copyright © 2016 Springer-Verlag
• First Published: First published in Communications in Mathematical Physics 349(3): 1063-1105
• Publisher Policy: Reproduced in accordance with the publisher copyright policy