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Integrable Systems, Shuffle Algebras, and Bethe Equations


Author: Boris L. Feigin
Translated by: V. E. Nazaikinskii
Original publication: Trudy Moskovskogo Matematicheskogo Obshchestva, tom 77 (2016), vypusk 2.
Journal: Trans. Moscow Math. Soc. 2016, 203-246
MSC (2010): Primary 17B37; Secondary 17B69, 17B80
DOI: https://doi.org/10.1090/mosc/259
Published electronically: November 28, 2016
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Abstract: We speak about the part of integrable system theory dealing with conformal theory and $ W$-algebras (ordinary and deformed). Some new approaches to finding Bethe equations that describe the spectrum of Hamiltonians of these quantum integrable systems are developed. The derivation of the Bethe equations is based on the technique of shuffle algebras arising in quantum group theory.


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Additional Information

Boris L. Feigin
Affiliation: National Research University Higher School of Economics, Moscow, Russia
Email: borfeigin@gmail.com

DOI: https://doi.org/10.1090/mosc/259
Keywords: Integrable system, shuffle algebra, Bethe equations, affine Lie algebra, center at the critical level, Drinfeld--Sokolov reduction, quantum group.
Published electronically: November 28, 2016
Additional Notes: This research was supported by the Russian Science Foundation (grant no. 16-11-10316).
Article copyright: © Copyright 2016 American Mathematical Society