Abstract:
The cactus group $J_n$, $n \geqslant 2$, can be generated by $n-1$ elements. In this paper, using the representation in these generators, we construct a linear representation of the cactus group. We prove that the image of the resulting representation is isomorphic to the permutation group $S_n$ and that for all $n \geqslant 3$, this representation is not faithful.
Keywords:cactus group, symmetric group, presentation by generators and relations, linear representation, faithful representation.
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