Some irreducible representations of the braid group B_n of dimension greater than n

TL;DR

This paper introduces a new family of finite-dimensional irreducible representations of the braid group B_n for n>3, including a subfamily with dimensions given by combinatorial numbers, expanding understanding of B_n's representation theory.

Contribution

It constructs a novel family of irreducible representations of B_n, generalizing the standard representation and parametrized by an integer m, with explicit dimension formulas.

Findings

A family of irreducible representations for B_n is constructed.

A subfamily with dimensions given by combinatorial numbers is identified.

The representation at m=1 recovers the standard representation.

Abstract

For any n>3, we give a family of finite dimensional irreducible representations of the braid group B_n. Moreover, we give a subfamily parametrized by 0<m<n of dimension the combinatoric number (n,m). The representation obtained in the case m=1 is equivalent to the Standard representation.