$E_7 \subset Sp(56,R)$ irrep decompositions of interest for physical models

TL;DR

This paper provides a method to derive the projection matrix for the $E_7$ subalgebra within the symplectic algebra $C_{28}$ and tabulates relevant decompositions for physical models.

Contribution

It introduces a way to compute the projection matrix for $E_7$ within $C_{28}$ and catalogs important irreducible decompositions for applications in physics.

Findings

Projection matrix for $E_7 o C_{28}$ obtained.

Decompositions of $C_{28}$ representations into $E_7$ irreps tabulated.

Results useful for modeling in theoretical physics.

Abstract

In this note we show how to obtain the projection matrix for the $E_7 \subset C_{28}$ chain and we tabulate some decompositions of the symplectic algebra $C_{28}$ representations into irreps of the $E_7$ subalgebra that are important for various physical models.