Generalized Long-Moody representations of braid groups

TL;DR

This paper explores generalizations of Long and Moody's method for constructing braid group representations, including new representations of subgroups like the pure braid group and the Hecke algebra, expanding the scope of braid group representation theory.

Contribution

It introduces novel generalizations of Long and Moody's construction, enabling representations of subgroups and algebraic structures related to braid groups.

Findings

Includes representations of subgroups such as the pure braid group.

Provides representations of the Hecke algebra.

Extends the applicability of Long-Moody constructions.

Abstract

Long and Moody gave a method of constructing representations of the braid group B_n. We discuss some ways to generalize their construction. One of these gives representations of subgroups of B_n, including the Gassner representation of the pure braid group as a special case. Another gives representations of the Hecke algebra.