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

2025/04/11 by Oshima, Toshio · 1 citation
#34M35 (Primary) 32S22 #58A17 (Secondary) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2504.09003

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.

Cited by

• Stable hyperplane arrangements

Related

• Long-Moody construction of braid group representations and Haraoka's multiplicative middle convolution for KZ-type equations
• Constructive Solutions to the Riemann--Hilbert Problem and Middle Convolution
• Classification of Fuchsian systems and their connection problem
• On the middle convolution
• On globally nilpotent differential equations