Braid group B_3 irreducibles, a DIY guide

TL;DR

This paper provides a method to construct a family of irreducible representations of the three-string braid group B_3 with customizable dimensions and family sizes, useful for researchers studying braid group representations.

Contribution

It offers a systematic construction approach for a broad class of irreducible B_3 representations, expanding the toolkit for algebraic and topological applications.

Findings

Constructs k(n)-dimensional families of irreducible representations

Allows customization of family size via an admissible function

Demonstrates explicit construction methods for B_3 representations

Abstract

This note tells you how to construct a k(n)-dimensional family of (isomorphism classes of) irreducible representations of dimension n for the three string braid group B_3, where k(n) is an admissible function of your choosing; for example take k(n) = [ n/2 ] +1 as in arXiv:0803.2778 and arXiv:0803.2785.