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arXiv · 2504.09003

Middle convolutions of KZ-type equations and single-elimination tournaments

Toshio Oshima
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Abstract

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.

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Toshio Oshima. 2025-04-11. Middle convolutions of KZ-type equations and single-elimination tournaments. https://arxiv.org/abs/2504.09003

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