English

Quantum generic Toda system

Mathematical Physics 2010-12-16 v1 High Energy Physics - Theory math.MP Exactly Solvable and Integrable Systems

Abstract

The Toda chains take a particular place in the theory of integrable systems, in contrast with the linear group structure for the Gaudin model this system is related to the corresponding Borel group and mediately to the geometry of flag varieties. The main goal of this paper is to reconstruct a "spectral curve" in a wider context of the generic Toda system. This appears to be an efficient way to find its quantization which is obtained here by the technique of quantum characteristic polynomial for the Gaudin model and an appropriate AKS reduction. We discuss also some relations of this result with the recent consideration of the Drinfeld Zastava space, the monopole space and corresponding Borel Yangian symmetries.

Keywords

Cite

@article{arxiv.1012.3296,
  title  = {Quantum generic Toda system},
  author = {D. Talalaev},
  journal= {arXiv preprint arXiv:1012.3296},
  year   = {2010}
}

Comments

9 pages

R2 v1 2026-06-21T16:59:01.307Z