$N$-Dimensional Representations of the Braid Groups $B_{N}$

Tong, Dian-Min; Yang, Shan-De; Ma, Zhong-Qi

$N$-Dimensional Representations of the Braid Groups $B_{N}$

Authors

Tong, Dian-Min

Yang, Shan-De

Ma, Zhong-Qi

Description

In this note, a new class of representations of the braid groups $B_{N}$ is constructed. It is proved that those representations contain three kinds of irreducible representations: the trivial (identity) one, the Burau one, and an $N$-dimensional one. The explicit form of the $N$-dimensional irreducible representation of the braid group $B_{N}$ is given here.