12 citations · 29 across the 10 of their papers we have counts for
9 papers · 1 filter
A local normal form for Hamiltonian actions of compact semisimple Poisson-Lie groups
Megumi Harada, Jeremy Lane, Aidan Patterson
The main contribution of this manuscript is a local normal form for Hamiltonian actions of Poisson-Lie groups on a symplectic manifold equipped with an -valued moment map,…
Stratified Gradient Hamiltonian Vector Fields and Collective Integrable Systems
Benjamin Hoffman, Jeremy Lane
We construct completely integrable systems on the dual of the Lie algebra of any compact Lie group with respect to the standard Lie-Poisson structure. These systems generalize…
Action-angle coordinates on coadjoint orbits and multiplicity free spaces from partial tropicalization
Anton Alekseev, Benjamin Hoffman, Jeremy Lane +1
Coadjoint orbits and multiplicity free spaces of compact Lie groups are important examples of symplectic manifolds with Hamiltonian groups actions. Constructing action-angle variab…
Local normal forms for multiplicity free actions on coadjoint orbits
Jeremy Lane
Actions of on coadjoint orbits via embeddings of into are an important family of examples of multiplicity free spaces. They are related to Gelfand-Z…
Concentration of symplectic volumes on Poisson homogeneous spaces
Anton Alekseev, Benjamin Hoffman, Jeremy Lane +1
For a compact Poisson-Lie group , the homogeneous space carries a family of symplectic forms , where is in the positive Weyl chamber and $s…
The Gelfand-Zeitlin system as a tropical limit of Ginzburg-Weinstein diffeomorphisms
Anton Alekseev, Jeremy Lane, Yanpeng Li
We show that the Ginzburg-Weinstein diffeomorphism of Alekseev-Meinrenken admits a scaling tropical limit on an open dense subset of $\mathfrak{u}(n)…
The geometric structure of symplectic contraction
Jeremy Lane
We show that the symplectic contraction map of Hilgert-Manon-Martens -- a symplectic version of Popov's horospherical contraction -- is simply the quotient of a Hamiltonian manifol…
Convexity and Thimm's Trick
Jeremy Lane
In this paper we prove a convexity and fibre-connectedness theorem for proper maps constructed by Thimm's trick on a connected Hamiltonian -space that generate a Hamiltonian…
Topological Monodromy of an Integrable Heisenberg Spin Chain
Jeremy Lane
We investigate topological properties of a completely integrable system on which was recently shown to have a Lagrangian fiber diffeomorphic to $\mathbb{…