Quantum representations of braid groups and holonomy Lie algebras

Kohno, Toshitake

doi:10.2969/aspm/07210117

VOL. 72 | 2017 Quantum representations of braid groups and holonomy Lie algebras

Toshitake Kohno

Editor(s) Taro Asuke, Shigenori Matsumoto, Yoshihiko Mitsumatsu

Adv. Stud. Pure Math., 2017: 117-144 (2017) DOI: 10.2969/aspm/07210117

Abstract

We review various aspects of representations of the holonomy Lie algebras and the associated monodromy representations of the fundamental groups for the complement of hyperplane arrangements. In particular, we describe the relation between monodromy representations of the KZ equation and homological representations of the braid groups by means of hypergeometric integrals.