Geodesic
Parabolic Orbits of 2-Nilpotent Elements for Classical Groups
Magdalena Boos1 ; Giovanni Cerulli Irelli2 ; Francesco Esposito3
1Faculty of Mathematics, Ruhr University, 44780 Bochum, Germany
2Department SBAI, Sapienza University, 00161 Rome, Italy
3Department of Mathematics, University of Padova, 35121 Padova, Italy
Journal of Lie Theory, Tome 29 (2019) no. 4, pp. 969-996

Voir la notice de l'article provenant de la source Heldermann Verlag

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

Magdalena Boos  1   ; Giovanni Cerulli Irelli  2   ; Francesco Esposito  3

1 Faculty of Mathematics, Ruhr University, 44780 Bochum, Germany
2 Department SBAI, Sapienza University, 00161 Rome, Italy
3 Department of Mathematics, University of Padova, 35121 Padova, Italy 
Magdalena Boos; Giovanni Cerulli Irelli; Francesco 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/JOLT_2019_29_4_a4/
@article{JOLT_2019_29_4_a4,
     author = {Magdalena Boos and Giovanni Cerulli Irelli and Francesco 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/JOLT_2019_29_4_a4/}
}
TY  - JOUR
AU  - Magdalena Boos
AU  - Giovanni Cerulli Irelli
AU  - Francesco Esposito
TI  - Parabolic Orbits of 2-Nilpotent Elements for Classical Groups
JO  - Journal of Lie Theory
PY  - 2019
SP  - 969
EP  - 996
VL  - 29
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/JOLT_2019_29_4_a4/
ID  - JOLT_2019_29_4_a4
ER  - 
%0 Journal Article
%A Magdalena Boos
%A Giovanni Cerulli Irelli
%A Francesco Esposito
%T Parabolic Orbits of 2-Nilpotent Elements for Classical Groups
%J Journal of Lie Theory
%D 2019
%P 969-996
%V 29
%N 4
%U http://geodesic.mathdoc.fr/item/JOLT_2019_29_4_a4/
%F JOLT_2019_29_4_a4