# Computing the real Weyl group

## TL;DR

This paper presents an explicit combinatorial method for computing the real Weyl group of a semisimple Lie algebra over the real numbers, aiding classification tasks relevant in physics.

## Contribution

It introduces a new combinatorial construction that allows efficient computation of the real Weyl group for semisimple Lie algebras.

## Key findings

- Provides an explicit combinatorial construction of the real Weyl group
- Enables efficient computation of the real Weyl group
- Facilitates classification of algebraic structures in physics

## Abstract

Let g be a semisimple Lie algebra over the real numbers. We describe an explicit combinatorial construction of the real Weyl group of g with respect to a given Cartan subalgebra. An efficient computation of this Weyl group is important for the classification of regular semisimple subalgebras, real carrier algebras, and real nilpotent orbits associated with g; the latter have various applications in theoretical physics.