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VOL. 52 | 2008 Remarks on the faithfulness of the Jones representations
Yasushi Kasahara

Editor(s) Robert Penner, Dieter Kotschick, Takashi Tsuboi, Nariya Kawazumi, Teruaki Kitano, Yoshihiko Mitsumatsu

Abstract

We consider the linear representations of the mapping class group of an $n$–punctured 2–sphere constructed by V. F. R. Jones using Iwahori–Hecke algebras of type A. We show that their faithfulness is equivalent to that of certain related Iwahori–Hecke algebra representation of Artin's braid group of $n-1$ strands. In the case of $n = 6$, we provide a further restriction for the kernel using our previous result, as well as a certain relation to the Burau representation of degree 4.

Information

Published: 1 January 2008
First available in Project Euclid: 28 November 2018

zbMATH: 1179.57029
MathSciNet: MR2509716

Digital Object Identifier: 10.2969/aspm/05210369

Rights: Copyright © 2008 Mathematical Society of Japan

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