Geodesic
Parabolic Orbits of 2-Nilpotent Elements for Classical Groups
Journal of Lie theory, Tome 29 (2019) no. 4, pp. 969-996
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We consider the conjugation-action of the Borel subgroup of the symplectic or the orthogonal group on the variety of nilpotent complex elements of nilpotency degree 2 in its Lie algebra. We translate the setup to a representation-theoretic context in the language of a symmetric quiver algebra. This makes it possible to provide a parametrization of the orbits via a combinatorial tool that we call symplectic/orthogonal oriented link patterns. We deduce information about numerology. We then generalize these classifications to standard parabolic subgroups for all classical groups. Finally, our results are restricted to the nilradical.
Classification : 14R20, 16N40, 17B45, 16G20, 16G70
Mots-clés : B-orbits, symmetric quiver, algebra with self-duality, combinatorial classification, Auslander-Reiten quiver 
@article{JLT_2019_29_4_JLT_2019_29_4_a4,
     author = {M. Boos and G. Cerulli Irelli and F. Esposito},
     title = {Parabolic {Orbits} of {2-Nilpotent} {Elements} for {Classical} {Groups}},
     journal = {Journal of Lie theory},
     pages = {969--996},
     year = {2019},
     volume = {29},
     number = {4},
     url = {http://geodesic.mathdoc.fr/item/JLT_2019_29_4_JLT_2019_29_4_a4/}
}
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M. Boos; G. Cerulli Irelli; F. Esposito. Parabolic Orbits of 2-Nilpotent Elements for Classical Groups. Journal of Lie theory, Tome 29 (2019) no. 4, pp. 969-996. http://geodesic.mathdoc.fr/item/JLT_2019_29_4_JLT_2019_29_4_a4/