Remarks on the faithfulness of the Jones representations

Yasushi Kasahara

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arXiv · 0803.0304

Remarks on the faithfulness of the Jones representations

Yasushi Kasahara

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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.

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Yasushi Kasahara. 2008-03-03. Remarks on the faithfulness of the Jones representations. https://arxiv.org/abs/0803.0304

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