Bowling ball representations of braid groups
Stephen Bigelow

TL;DR
This paper extends Jones's bowling ball metaphor for braid groups to multiple balls, leading to new algebraic representations including the Iwahori-Hecke algebra and a cabled Temperley-Lieb version.
Contribution
It introduces a multi-ball extension of the bowling ball model, resulting in novel algebraic representations of braid groups.
Findings
Derived the Iwahori-Hecke algebra from the extended model
Constructed a cabled Temperley-Lieb representation
Enhanced understanding of braid group representations
Abstract
In a remark in his seminal 1987 paper, Jones describes a way to define the Burau matrix of a positive braid using a metaphor of bowling a ball down a bowling alley with braided lanes. We extend this definition to allow multiple bowling balls to be bowled simultaneously. We obtain the Iwahori-Hecke algebra and a cabled version of the Temperley-Lieb representation.
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