20 citations · 21 across the 4 of their papers we have counts for
8 papers
A symplectic approach to van den Ban's convexity theorem
Philip Foth, Michael Otto
Let G be a complex semisimple Lie group and τa complex antilinear involution that commutes with the Cartan involution. If H denotes the connected subgroup of τ-fixed points in G, a…
Toric degenerations of weight varieties and applications
Philip Foth, Yi Hu
We show that a weight variety, which is a quotient of a flag variety by the maximal torus, admits a flat degeneration to a toric variety. In particular, we show that the moduli spa…
Poisson structures on complex flag manifolds associated with real forms
Philip Foth, Jiang-Hua Lu
For a complex semi-simple group G and its real form G0 we define a Poisson structure on the flag variety of G such that all the Bruhat cells (for a suitable choice of a Borel subgr…
A note on Lagrangian loci of quotients
Philip Foth
We study hamiltonian actions of compact groups in the presence of compatible involutions. We show that the lagrangian fixed point set on the symplectically reduced space is isomorp…
The Geometry of Polygons in R^5 and Quaternions
Philip Foth, Guadalupe Lozano
We consider the moduli space M_r of polygons with fixed side lengths in five-dimensional eucledian space. We analyze the local structure of its singularities and exhibit a real-ana…
Geometry of Four-vector Fields on Quaternionic Flag Manifolds
Philip Foth, Frederick Leitner
The purpose of this paper is to describe certain natural 4-vector fields on quaternionic flag manifolds, which geometrically determine the Bruhat cell decomposition. This structure…