Irreducible representations of Braid Group $B_n$ of dimension $n+1$

TL;DR

This paper proves that for braid groups with n ≥ 10, there are no irreducible representations of dimension n+1, establishing a new limitation on the representation theory of braid groups.

Contribution

It demonstrates a non-existence result for irreducible representations of specific dimensions in braid groups for n ≥ 10.

Findings

No irreducible representations of dimension n+1 for B_n when n ≥ 10

Provides new constraints on the representation theory of braid groups

Advances understanding of the structure of B_n representations

Abstract

We prove that there are no irreducible representations of $B_n$ of dimension $n+1$ for $n\geq 10.$