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Rigidity of Kac–Schwarz operators

Abstract

In his work on the mathematical formulation of 2d quantum gravity Schwarz established a rigidity result for Kac–Schwarz operators for the n-KdV hierarchies. Later on, Adler and van Moerbeke as well as Fastré obtained different proofs of this result. We give yet another proof of the rigidity, one that in fact holds for all Drinfeld–Sokolov hierarchies.

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Acknowledgements

It is a great pleasure to thank Mattia Cafasso, Albert Schwarz, and the referees for very helpful exchanges and comments.

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Correspondence to Martin T. Luu.

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Luu, M.T. Rigidity of Kac–Schwarz operators. Lett Math Phys 110, 911–924 (2020). https://doi.org/10.1007/s11005-019-01242-3

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  • DOI: https://doi.org/10.1007/s11005-019-01242-3

Keywords

  • Kac–Schwarz operators
  • 2D quantum gravity
  • Sato Grassmannian
  • Drinfeld–Sokolov hierarchies

Mathematics Subject Classification

  • 81T40
  • 37K10
  • 17B67