Classification of Admissible Nilpotent Orbits in Simple Real Lie Algebras E6(6) and E6(−26)

Prehomogeneous Spaces Associated with Nilpotent Orbits in Simple Real Lie Algebras E6(6) and E6(-26) and Their Relative Invariants

ADMISSIBLE NILPOTENT ORBITS OF REAL AND p-ADIC SPLIT EXCEPTIONAL GROUPS

We determine the admissible nilpotent coadjoint orbits of real and p-adic split exceptional groups of types G2, F4, E6 and E7. We find that all Lusztig-Spaltenstein special orbits are admissible. Moreover, there exist nonspecial admissible orbits, corresponding to “completely odd” orbits in Lusztig’s special pieces. In addition, we determine the number of, and representatives for, the non-even ...

Classification of Admissible Nilpotent Orbits in Simple Exceptional Real Lie Algebras of Inner Type

In this paper we give a classification of admissible nilpotent orbits of the noncompact simple exceptional real Lie groups of inner type. We use a lemma of Takuya Ohta and some information from the work of Dragomir Djoković to construct a simple algorithm which allows us to decide the admissiblity of a given orbit.

Series of Nilpotent Orbits

We organize the nilpotent orbits in the exceptional complex Lie algebras into series and show that within each series the dimension of the orbit is a linear function of the natural parameter a = 1, 2, 4, 8, respectively for f4, e6, e7, e8. We observe similar regularities for the centralizers of nilpotent elements in a series and graded components in the associated grading of the ambient Lie alg...

On 1-dimensional Representations of Finite W -algebras Associated to Simple Lie Algebras of Exceptional Type

We consider the finite W -algebra U(g, e) associated to a nilpotent element e ∈ g in a simple complex Lie algebra g of exceptional type. Using presentations obtained through an algorithm based on the PBW-theorem, we verify a conjecture of Premet, that U(g, e) always has a 1-dimensional representation, when g is of type G2, F4, E6 or E7. Thanks to a theorem of Premet, this allows one to deduce t...