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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.09003 |
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| _version_ | 1866910909697359872 |
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| author | Oshima, Toshio |
| author_facet | Oshima, Toshio |
| contents | We introduce an extension of the generalized Riemann scheme for Fuchsian ordinary differential equations in the case of KZ-type equations. This extension describes the local structure of equations obtained by resolving the singularities of KZ-type equations. We present the transformation of this extension under middle convolutions. As a consequence, we derive the corresponding transformation of the eigenvalues and multiplicities of the residue matrices of KZ-type equations under middle convolutions. We interpret the result in terms of the combinatorics of single-elimination tournaments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_09003 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Middle convolutions of KZ-type equations and single-elimination tournaments Oshima, Toshio Classical Analysis and ODEs 34M35 (Primary) 32S22, 58A17 (Secondary) We introduce an extension of the generalized Riemann scheme for Fuchsian ordinary differential equations in the case of KZ-type equations. This extension describes the local structure of equations obtained by resolving the singularities of KZ-type equations. We present the transformation of this extension under middle convolutions. As a consequence, we derive the corresponding transformation of the eigenvalues and multiplicities of the residue matrices of KZ-type equations under middle convolutions. We interpret the result in terms of the combinatorics of single-elimination tournaments. |
| title | Middle convolutions of KZ-type equations and single-elimination tournaments |
| topic | Classical Analysis and ODEs 34M35 (Primary) 32S22, 58A17 (Secondary) |
| url | https://arxiv.org/abs/2504.09003 |