Multiplicative middle convolution for KZ equations

We extend the middle convolution for monodromy of Fuchsian ordinary differential equations due to Katz to an operation for monodromy of KZ equations. This operation, also called the middle convolution, gives a monodromy of KZ equation obtained by the additive middle convolution. Since the fundamenta...

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Bibliographic Details
Published in:Mathematische Zeitschrift 2020-04, Vol.294 (3-4), p.1787-1839
Main Author: Haraoka, Yoshishige
Format: Article
Language:English
Subjects:
Braid theory
Braiding
Convolution
Differential equations
Mathematical analysis
Mathematics
Mathematics and Statistics
Ordinary differential equations
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Summary:We extend the middle convolution for monodromy of Fuchsian ordinary differential equations due to Katz to an operation for monodromy of KZ equations. This operation, also called the middle convolution, gives a monodromy of KZ equation obtained by the additive middle convolution. Since the fundamental group of the domain of definition of KZ equation is the pure braid group, our middle convolution also gives a recursive way of constructing irreducible representations of the pure braid group. Several applications are considered.
ISSN:0025-5874
1432-1823
DOI:10.1007/s00209-019-02322-9