112 citations · 144 across the 22 of their papers we have counts for
8 papers · 1 filter
Computing component groups of stabilizers of nilpotent orbit representatives
Emanuele Di Bella, Willem A. De Graaf
The theory of nilpotent orbits of simple Lie algebras has seen tremendous developments over the past decades. In this context an important role is played by the component group of…
Computing Galois cohomology of a real linear algebraic group
Mikhail Borovoi, Willem A. de Graaf
Let G be a linear algebraic group, not necessarily connected or reductive, over the field of real numbers R. We describe a method, implemented on computer, to find the first Galois…
Exploring Lie theory with GAP
Willem A. de Graaf
We illustrate the Lie theoretic capabilities of the computational algebra system GAP4 by reporting on results on nilpotent orbits of simple Lie algebras that have been obtained usi…
Semisimple elements and the little Weyl group of real semisimple -graded Lie algebras
Willem de Graaf, Hông Vân Lê
We consider the semisimple orbits of a Vinberg -representation. First we take the complex numbers as base field. By a case by case analysis we show a technical result stating th…
Nilpotent orbits in real symmetric pairs and stationary black holes
Heiko Dietrich, Willem A. de Graaf, Daniele Ruggeri +1
In the classification of stationary solutions in extended supergravities with symmetric scalar manifolds, the nilpotent orbits of a real symmetric pair play an important role. In t…
Regular subalgebras and nilpotent orbits of real graded Lie algebras
H. Dietrich, Paolo Faccin, Willem A. de Graaf
For a semisimple Lie algebra over the complex numbers, Dynkin (1952) developed an algorithm to classify the regular semisimple subalgebras, up to conjugacy by the inner automorphis…
irrep decompositions of interest for physical models
Lorenzo Fortunato, Willem A. de Graaf
In this note we show how to obtain the projection matrix for the chain and we tabulate some decompositions of the symplectic algebra representations i…
Good index behaviour of -representations, I
Willem A. de Graaf, Oksana S. Yakimova
Let be an algebraic group with $q=\Lie Q$ and a -module. The index of is the minimal codimension of the -orbits in the dual space . There is a general inequa…