215 citations · 807 across the 39 of their papers we have counts for
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(Quasi-)Hamiltonian manifolds of cohomogeneity one
Friedrich Knop, Kay Paulus
We classify compact, connected Hamiltonian and quasi-Hamiltonian manifolds of cohomogeneity one (which is the same as being multiplicity free of rank one). Here the group acting is…
Multiplicity free quasi-Hamiltonian manifolds
Friedrich Knop
A (quasi-)Hamiltonian manifold is called multiplicity free if all of its symplectic reductions are 0-dimensional. In this paper, we classify multiplicity free Hamiltonian actions f…
Automorphisms of multiplicity free Hamiltonian manifolds
Friedrich Knop
We compute the sheaf of automorphisms of a multiplicity free Hamiltonian manifold over its momentum polytope and show that its higher cohomology groups vanish. Together with a theo…
Classification of multiplicity free symplectic representations
Friedrich Knop
Let G be a connected reductive group acting on a finite dimensional vector space V. Assume that V is equipped with a G-invariant symplectic form. Then the ring C[V] of polynomial f…
Convexity of Hamiltonian manifolds
Friedrich Knop
Let K be a connected Lie group and M a Hamiltonian K-manifold. In this paper, we introduce the notion of convexity of M. It implies that the momentum image is convex, the moment ma…