## Advanced Studies in Pure Mathematics

### Remarks on the faithfulness of the Jones representations

Yasushi Kasahara

#### 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.

#### Article information

Dates
Revised: 23 October 2007
First available in Project Euclid: 28 November 2018

https://projecteuclid.org/ euclid.aspm/1543447489

Digital Object Identifier
doi:10.2969/aspm/05210369

Mathematical Reviews number (MathSciNet)
MR2509716

Zentralblatt MATH identifier
1179.57029

#### Citation

Kasahara, Yasushi. Remarks on the faithfulness of the Jones representations. Groups of Diffeomorphisms: In honor of Shigeyuki Morita on the occasion of his 60th birthday, 369--381, Mathematical Society of Japan, Tokyo, Japan, 2008. doi:10.2969/aspm/05210369. https://projecteuclid.org/euclid.aspm/1543447489