6 papers
Quantum gates from the middle convolution of twisted Burau representations
Haru Negami
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…
Finite images of braid group representations and algebraic solutions of KZ-type equations
Haru Negami
Finite monodromy provides a bridge between group representations and algebraic solutions of differential equations. We study this connection for the Katz-Long-Moody construction, w…
A closed signature formula for the Katz-Long-Moody Hermitian form
Haru Negami
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…
Hecke algebra representations from the Katz-Long-Moody construction
Haru Negami
We study the Katz-Long-Moody (KLM) construction and classify exactly when the resulting braid group representations factor through Hecke algebras, for scalar braid part and semisim…
Long-Moody construction of braid group representations and Haraoka's multiplicative middle convolution for KZ-type equations
Haru Negami
We establish a correspondence between the algebraic and analytic approaches to constructing representations of the braid group Bn: the Katz--Long--Moody construction and the multip…
Long-Moody construction of braid representations and Katz middle convolution
Kazuki Hiroe, Haru Negami
The Long-Moody construction is a method to obtain representations of braid groups introduced by Long and Moody. Also the Katz middle convolution is known to be a method to construc…