Journal of Lie Theory

no. 1
A structure theorem along fibers of extreme points of the momentum polytope
Heinzner, Peter1; Zöller, Christian1
1Fakultät für Mathematik, Ruhr Universität Bochum, Universitätsstrasse 150, 44780 Bochum, Deutschland
Journal of Lie Theory, Special issue dedicated to the memory of Joseph A. Wolf, Volume 36 (2026) no. 1, pp. 51-76

Let $G$ be a complex reductive Lie group acting on a compact Kähler manifold $X$. Assume that the action of a maximal compact subgroup $K$ of $G$ is Hamiltonian. For each extreme point of the convex hull of the momentum map image, there exists an associated open dense subset of $X$, that is invariant under the action of a parabolic subgroup $Q$ of $G$. We prove a $Q$-equivariant product decomposition for the $Q$-action on this subset and discuss some applications of this result. Additionaly, we establish a similar statement for real reductive subgroups of $G$ and the restricted momentum map.

Received:
Accepted:
Published online:
DOI: 10.5802/jolt.1419

Heinzner, Peter  1 ; Zöller, Christian  1

1 Fakultät für Mathematik, Ruhr Universität Bochum, Universitätsstrasse 150, 44780 Bochum, Deutschland 
Heinzner, Peter; Zöller, Christian. A structure theorem along fibers of extreme points of the momentum polytope. Journal of Lie Theory, Special issue dedicated to the memory of Joseph A. Wolf, Volume 36 (2026) no. 1, pp. 51-76. doi: 10.5802/jolt.1419
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