Advanced Studies in Pure Mathematics

Quantum representations of braid groups and holonomy Lie algebras

Toshitake Kohno

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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.

Article information

Source
Geometry, Dynamics, and Foliations 2013: In honor of Steven Hurder and Takashi Tsuboi on the occasion of their 60th birthdays, T. Asuke, S. Matsumoto and Y. Mitsumatsu, eds. (Tokyo: Mathematical Society of Japan, 2017), 117-144

Dates
Received: 18 August 2014
Revised: 26 December 2014
First available in Project Euclid: 4 October 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1538671764

Digital Object Identifier
doi:10.2969/aspm/07210117

Mathematical Reviews number (MathSciNet)
MR3726707

Zentralblatt MATH identifier
06843303

Subjects
Primary: 52C35: Arrangements of points, flats, hyperplanes [See also 32S22] 20F36: Braid groups; Artin groups 57M07: Topological methods in group theory 55P62: Rational homotopy theory 33C60: Hypergeometric integrals and functions defined by them ($E$, $G$, $H$ and $I$ functions) 17B37: Quantum groups (quantized enveloping algebras) and related deformations [See also 16T20, 20G42, 81R50, 82B23]

Citation

Kohno, Toshitake. Quantum representations of braid groups and holonomy Lie algebras. Geometry, Dynamics, and Foliations 2013: In honor of Steven Hurder and Takashi Tsuboi on the occasion of their 60th birthdays, 117--144, Mathematical Society of Japan, Tokyo, Japan, 2017. doi:10.2969/aspm/07210117. https://projecteuclid.org/euclid.aspm/1538671764


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