Fusion of SO(N) reflection matrices

TL;DR

This paper investigates the fusion process of SO(N) reflection matrices, deriving the reflection matrix for rank two particle multiplets from the fundamental vector multiplet, and analyzes its decomposition.

Contribution

It introduces a method to fuse SO(N) reflection matrices and provides the explicit form and decomposition for higher-rank multiplets.

Findings

Derived the reflection matrix for rank two multiplets from fundamental ones.

Provided the decomposition of the fused reflection matrix.

Enhanced understanding of boundary scattering in SO(N) symmetric models.

Abstract

We examine the reflection matrix acting on the $SO(N)$ vector multiplet and fuse it to obtain that acting on the rank two particle multiplet, and give its decomposition.