## Advanced Studies in Pure Mathematics

- Adv. Stud. Pure Math.
- Groups of Diffeomorphisms: In honor of Shigeyuki Morita on the occasion of his 60th birthday, R. Penner, D. Kotschick, T. Tsuboi, N. Kawazumi, T. Kitano and Y. Mitsumatsu, eds. (Tokyo: Mathematical Society of Japan, 2008), 369 - 381

### Remarks on the faithfulness of the Jones representations

#### 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**

Received: 30 April 2007

Revised: 23 October 2007

First available in Project Euclid:
28 November 2018

**Permanent link to this document**

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