In this paper, we show that the Ginzburg–Weinstein diffeomorphism of Alekseev &
Meinrenken (Alekseev, Meinrenken 2007 J. Differential Geom. 76, 1–34.(10.4310/jdg …

Coadjoint orbits and multiplicity free spaces of compact Lie groups are important examples
of symplectic manifolds with Hamiltonian groups actions. Constructing action-angle …

For a compact Poisson-Lie group $ K $, the homogeneous space $ K/T $ carries a family of
symplectic forms $\omega_\xi^ s $, where $\xi\in\mathfrak {t}^* _+ $ is in the positive Weyl …

Let G be a connected semisimple Lie group. There are two natural duality constructions that
assign to G: its Langlands dual group G^ ∨ G∨, and its Poisson–Lie dual group G^* G∗ …

Let G be a connected and simply connected complex semisimple Lie group. For a collection
of homogeneous G-spaces G/Q, we construct a finite atlas A _\scriptscriptstyle BS (G/Q) A …

In this paper, we introduce geometric multiplicities, which are positive varieties with potential
fibered over the Cartan subgroup $ H $ of a reductive group $ G $. They form a monoidal …

In this thesis, we study Poisson geometry and representation theory by using the approach
of geometrization and tropicalization. The goal is to find relations between some new …

It was recently shown by [1] that in the t→∞ limit of certain t-dependent coordinates (cluster
coordinates given by generalized minors), the Poisson bracket on the dual Poisson Lie …