Computing the real Weyl group. (May 2021)

• Record Type: Journal Article
• Authors: Dietrich, Heiko; de Graaf, Willem A.
• Is Part Of: Journal of symbolic computation. Volume 104(2021)
• Page Start: 1
• Page End: 14
• Publication Date: 2021-05
• Subjects: Real Weyl group -- Real semisimple Lie algebra -- Computational Lie theory; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2020.04.001
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: Let g be a semisimple Lie algebra over the field of real numbers. Let G be a real Lie group with Lie algebra g . The real Weyl group of G with respect to a Cartan subalgebra h of g is defined as W ( G, h ) = N G ( h ) / Z G ( h ) . We describe an explicit construction of W ( G, h ) for Lie groups G that arise as the set of real points of connected algebraic groups. We show that this also gives a construction of W ( G, h ) when G is the adjoint group of g . This algorithm 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.