Author

Haru Negami

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Preprint Sep 2026

Quantum gates from the middle convolution of twisted Burau representations

We study braid representations obtained from character-twisted Burau inputs by the Katz-Long-Moody (KLM) construction, which corresponds to multiplicative middle convolution for KZ-type equations. For $n\ge2$, let $q=e^{2\pi ia}$, $\tau=e^{2\pi ic}$, where $a,c>0$ and $nc+(n+1)a<1$. Known form and signature results giv...

Haru Negami · 0 citations

Preprint Sep 2026

A closed signature formula for the Katz-Long-Moody Hermitian form

The Katz-Long-Moody construction associates to a representation of the semidirect product of a free group and a braid group, defined by the Artin action, and a nonzero parameter a new representation of the same group. On the pure braid group it corresponds to Haraoka's multiplicative middle convolution for KZ-type equa...

Haru Negami · 1 citation

Preprint Sep 2026

Finite images of braid group representations and algebraic solutions of KZ-type equations

Finite monodromy provides a bridge between group representations and algebraic solutions of differential equations. We study this connection for the Katz-Long-Moody construction, which transforms representations of the semidirect product of a free group and a braid group into new representations of the same group and i...

Haru Negami · 0 citations