arXiv subjects

Henrik Stoetzel

Publications and source records attributed to Henrik Stoetzel.

5 recordsLinked to original sources

arXiv2012

Stratifications with respect to actions of real reductive groups

We study the action of a real reductive group G on a real submanifold X of a K"ahler manifold Z. We suppose that the action of G extends holomorphically to an action of a complex reductive group and is Hamiltonian with respect to a compatible maximal compact subgroup of the complex reductive group. There is a corresponding gradient map obtained from a Cartan decomposition of G. We obtain a Morse like function on X. Associated to its critical points are various sets of semistable points which we study in great detail. In particular, we have G-stable submanifolds of X which are called pre-strata. In case that the gradient map is proper, the pre-strata form a decomposition of X and in case that X is compact they are the strata of a Morse type stratification of X. Our results are generalizations of results of Kirwan obtained in the case that X=Z is compact and the group itself is complex reductive.

math.CV↗

arXiv2009

Spherical gradient manifolds

We study the action of a real-reductive group $G=K\exp(\lie{p})$ on real-analytic submanifold $X$ of a Kähler manifold $Z$. We suppose that the action of $G$ extends holomorphically to an action of the complexified group $G^\mbb{C}$ such that the action of a maximal Hamiltonian subgroup is Hamiltonian. The moment map $μ$ induces a gradient map $μ_\lie{p}\colon X\to\lie{p}$. We show that $μ_\lie{p}$ almost separates the $K$--orbits if and only if a minimal parabolic subgroup of $G$ has an open orbit. This generalizes Brion's characterization of spherical Kähler manifolds with moment maps.

math.RT↗

arXiv2009

Closed orbits of real reductive representations

We prove that the set of closed orbits in a real reductive representation contains a subset which is open with respect to the real Zariski topology if it has non-empty interior. In particular the set of closed orbits is dense.

math.RT↗

arXiv2008

A Quotient Restriction Theorem for actions of real reductive groups

We prove a version of the Chevalley Restriction Theorem for the action of a real reductive group G on a topological space X which locally embeds into a holomorphic representation. Assuming that there exists an appropriate quotient X//G for the G-action, we introduce a stratification which is defined with respect to orbit types of closed orbits. Our main result is a description of the quotient X//G in terms of quotients by normalizer subgroups associated to the stratification.

math.RT↗

arXiv2005

Semistable points with respect to real forms

We consider actions of real Lie subgroups G of complex reductive Lie groups on Kaehlerian spaces. Our main result is the openness of the set of semistable points with respect to a momentum map and the action of G.

math.CV↗