# Irreducibility of quantum representations of mapping class groups with boundary

## TL;DR

This paper proves that certain quantum representations of mapping class groups are always irreducible when the surface has boundary points, extending previous results to more general cases.

## Contribution

It generalizes Roberts' irreducibility result to surfaces with boundary points colored by specific labels in the context of SU(2) quantum representations.

## Key findings

- Quantum representations are irreducible with boundary points.
- Irreducibility holds when at least one boundary point is colored by one.
- Generalizes previous irreducibility results to new surface configurations.

## Abstract

We prove that the Witten--Reshetikhin--Turaev $\mathrm{SU}(2)$ quantum representations of mapping class groups are always irreducible in the case of surfaces equipped with colored banded points, provided that at least one banded point is colored by one. We thus generalize a well--known result due to J. Roberts.