English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Coadjoint orbits and multiplicity free spaces of compact Lie groups areimportant examples of symplectic manifolds with Hamiltonian groups actions.Constructing action-angle variables on these spaces is a challenging task. Afundamental result in the field is the Guillemin-Sternberg construction ofGelfand-Zeitlin integrable systems for the groups $K=U(n), SO(n)$. Extendingthese results to groups of other types is one of the goals of this paper.  Partial tropicalizations are Poisson spaces with constant Poisson bracketbuilt using techniques of Poisson-Lie theory and the geometric crystals ofBerenstein-Kazhdan. They provide a bridge between dual spaces of Lie algebras${\rm Lie}(K)^*$ with linear Poisson brackets and polyhedral cones whichparametrize the canonical bases of irreducible modules of $G=K^\mathbb{C}$.  We generalize the construction of partial tropicalizations to allow forarbitrary cluster charts, and apply it to questions in symplectic geometry. Foreach regular coadjoint orbit of a compact group $K$, we construct an exhaustionby symplectic embeddings of toric domains. As a by product we arrive at aconjectured formula for Gromov width of regular coadjoint orbits. We provesimilar results for multiplicity free $K$-spaces.

Action-angle coordinates on coadjoint orbits and multiplicity free spaces from partial tropicalization