Quantum KdV hierarchy and shifted symmetric functions
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866915254278029312 |
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| author | van Ittersum, Jan-Willem Ruzza, Giulio |
| author_facet | van Ittersum, Jan-Willem Ruzza, Giulio |
| contents | We study spectral properties of the quantum Korteweg-de Vries hierarchy defined by Buryak and Rossi. We prove that eigenvalues to first order in the dispersion parameter are given by shifted symmetric functions. The proof is based on the boson-fermion correspondence and an analysis of quartic expressions in fermions. As an application, we obtain a closed evaluation of certain double Hodge integrals on the moduli spaces of curves. Finally, we provide an explicit formula for the eigenvectors to first order in the dispersion parameter. In particular, we show that its Schur expansion is supported on partitions for which the Hamming distance is minimal. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_02266 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quantum KdV hierarchy and shifted symmetric functions van Ittersum, Jan-Willem Ruzza, Giulio Mathematical Physics 05A17, 14H70, 37K10 We study spectral properties of the quantum Korteweg-de Vries hierarchy defined by Buryak and Rossi. We prove that eigenvalues to first order in the dispersion parameter are given by shifted symmetric functions. The proof is based on the boson-fermion correspondence and an analysis of quartic expressions in fermions. As an application, we obtain a closed evaluation of certain double Hodge integrals on the moduli spaces of curves. Finally, we provide an explicit formula for the eigenvectors to first order in the dispersion parameter. In particular, we show that its Schur expansion is supported on partitions for which the Hamming distance is minimal. |
| title | Quantum KdV hierarchy and shifted symmetric functions |
| topic | Mathematical Physics 05A17, 14H70, 37K10 |
| url | https://arxiv.org/abs/2407.02266 |