Upper triangular parts of conjugacy classes of nilpotent matrices with finite number of B-orbits

Lucas Fresse (1)

1 IECL - Institut Élie Cartan de Lorraine

We consider the intersection of the conjugacy class of a nilpotent matrix with the space of upper triangular matrices. We give necessary and sufficient conditions for this intersection to be a union of finitely many orbits for the action by conjugation of the group of invertible upper triangular matrices.

Mots clés: nilpotent matrices; nilpotent orbits; spherical varieties; orbital varieties

Domaines: Géométrie algébrique [math.AG]; Théorie des groupes [math.GR]; Théorie des représentations [math.RT]

Lucas Fresse. Upper triangular parts of conjugacy classes of nilpotent matrices with finite number of B-orbits. Journal of the Mathematical Society of Japan, 2013, 65 (3), pp.967-992. ⟨10.2969/jmsj/06530967⟩. ⟨hal-01281865⟩