On the spectral problem of the quantum KdV hierarchy

@article{Ruzza2021OnTS,
  title={On the spectral problem of the quantum KdV hierarchy},
  author={Giulio Ruzza and Di Yang},
  journal={Journal of Physics A: Mathematical and Theoretical},
  year={2021},
  volume={54}
}
  • G. Ruzza, Di Yang
  • Published 3 April 2021
  • Mathematics, Physics
  • Journal of Physics A: Mathematical and Theoretical
The spectral problem for the quantum dispersionless Korteweg–de Vries (KdV) hierarchy, aka the quantum Hopf hierarchy, is solved by Dubrovin. In this article, following Dubrovin, we study Buryak–Rossi’s quantum KdV hierarchy. In particular, we prove a symmetry property and a non-degeneracy property for the quantum KdV Hamiltonians. On the basis of this we construct a complete set of common eigenvectors. The analysis underlying this spectral problem implies certain vanishing identities for… 
Quantum KdV hierarchy and quasimodular forms
Dubrovin [10] has shown that the spectrum of the quantization (with respect to the first Poisson structure) of the dispersionless Korteweg–de Vries (KdV) hierarchy is given by shifted symmetric

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