Parabolic Conjugation and Commuting Varieties

Magdalena Boos (1) , Michael Bulois (2)

1 Fakultät für Mathematik [Bochum]
2 AGL - Algèbre, géométrie, logique

We consider the conjugation-action of an arbitrary upper-block parabolic subgroup of the general linear group on the variety of nilpotent matrices in its Lie algebra. Lie-theoretically, it is natural to wonder about the number of orbits of this action. We translate the setup to a representation-theoretic one and obtain a finiteness criterion which classifies all actions with only a finite number of orbits over an arbitrary infinite field. These results are applied to commuting varieties and nested punctual Hilbert schemes.

Mots clés: quiver with relation; finite representation type; parabolic algebra; hilbert scheme; commuting variety

Domaines: Théorie des représentations [math.RT]

Magdalena Boos, Michael Bulois. Parabolic Conjugation and Commuting Varieties. Transformation Groups, 2019, Parabolic Conjugation and Commuting Varieties, ⟨10.1007/s00031-018-9507-4⟩. ⟨hal-01498381⟩