A note on certain finite-dimensional representations of the braid group

TL;DR

This paper explicitly classifies all finite-dimensional irreducible representations of certain permutation groups that are images of the Artin braid group, enhancing understanding of braid group representations.

Contribution

It provides a complete explicit classification of finite-dimensional irreducible representations for a specific class of permutation groups related to the braid group.

Findings

Explicit descriptions of all such irreducible representations

Identification of the permutation groups as homomorphic images of the braid group

Enhanced understanding of the structure of braid group representations

Abstract

In this paper the author finds explicitly all finite-dimensional irreducible representations of a series of finite permutation groups that are homomorphic images of Artin braid group.