相关论文: Symplectic and Hamiltonian properties of holomorph…

We study the symplectic structure of the holomorphic coadjoint orbits, generalizing a theorem of McDuff on the symplectic structure of Hermitian symmetric spaces of noncompact type.

This paper is devoted to the construction of a hyperkaehler structure on the complexification of any Hermitian-symmetric affine coadjoint orbit O of a semi-simple L*-group of compact type, which is compatible with the complex symplectic…

For a complex Lie group $G$ with a real form $G_0\subset G$, we prove that any Hamiltionian automorphism $\phi$ of a coadjoint orbit $\mathcal O_0$ of $G_0$ whose connected components are simply connected, may be approximated by holomorphic…

Let G be a simple, noncompact, connected, real Lie group with finite center, and K a maximal compact subgroup of G. We assume that G/K is Hermitian. Using GIT methods derived from the generalized eigenvalue problem, we compute a set of…

In the finite-dimensional setting, every Hermitian-symmetric space of compact type is a coadjoint orbit of a finite-dimensional Lie group. It is natural to ask whether every infinite-dimensional Hermitian-symmetric space of compact type,…

We prove that any coadjoint orbit with real eigenvalues of a complex semisimple Lie group, equipped with the real part of the canonical holomorphic symplectic form, is symplectomorphic to the cotangent bundle of a (partial) flag manifold.…

Let ${\cal O}$ be a quantizable coadjoint orbit of a semisimple Lie group $G$. Under certain hypotheses we prove that $#(\pi_1(\text{Ham}({\cal O})))\geq #(Z(G))$, where $\text{Ham}({\cal O})$ is the group of Hamiltonian symplectomorphisms…

Orbits of coadjoint representations of classical compact Lie groups have a lot of applications. They appear in representation theory, geometrical quantization, theory of magnetism, quantum optics etc. As geometric objects the orbits were…

Let mathcal{O}_lambda be a generic coadjoint orbit of a compact semi-simple Lie group K. Weight varieties are the symplectic reductions of mathcal{O}_lambda by the maximal torus T in K. We use a theorem of Tolman and Weitsman to compute the…

We give a classification of generic coadjoint orbits for the groups of symplectomorphisms and Hamiltonian diffeomorphisms of a closed symplectic surface. We also classify simple Morse functions on symplectic surfaces with respect to actions…

There is a known hyperk\"ahler structure on any complexified Hermitian symmetric space $G/K$, whose construction relies on identifying $G/K$ with both a (co)adjoint orbit and the cotangent bundle to the compact Hermitian symmetric space…

We classify generic coadjoint orbits for symplectomorphism groups of compact symplectic surfaces with or without boundary. We also classify simple Morse functions on such surfaces up to a symplectomorphism.

This paper describes two real analytic symplectomorphisms defined on appropriate dense open subsets of any coadjoint orbit of a compact semisimple Lie algebra. The first symplectomorphism sends the open dense subset to a bounded subset of a…

Let $\mathrm{SL}(n,\mathbb{R})$ be the special linear group and $\mathfrak{sl}(n,\mathbb{R})$ its Lie algebra. We study geometric properties associated to the adjoint orbits in the simplest non-trivial case, namely, those of…

This expository article is an introduction to the adjoint orbits of complex semisimple groups, primarily in the algebro-geometric and Lie-theoretic contexts, and with a pronounced emphasis on the properties of semisimple and nilpotent…

As we said in our previous work [4], the main idea of our research is to introduce a class of Lie groupoids by means of co-adjoint representation of a Lie groupoid on its isotropy Lie algebroid, which we called coadjoint Lie groupoids. In…

Let G be an n-dimensional semisimple compact and connected Lie group acting on both the Lie algebra g of G and its dual g*. We show that a nondegenerate Killing form of G induces an Ad*-equivariant isomorphism of g onto g* which, in turn,…

Semisimple (co)adjoint orbits through real hyperbolic elements are well-known to be symplectomorphic to cotangent bundles. We provide a new proof of this fact based on elementary results on both Lie theory and symplectic geometry. Our proof…

Let G be a compact connected Lie group G and T its maximal torus. The coadjoint orbit O_lambda through lambda in Lie(T)^* is canonically a symplectic manifold. Therefore we can ask the question about its Gromov width. In many known cases…

For a Lie groupoid $\mathcal{G}$ with Lie algebroid $A$, we realize the symplectic leaves of the Lie-Poisson structure on $A^*$ as orbits of the affine coadjoint action of the Lie groupoid $\mathcal{J}\mathcal{G}\ltimes T^*M$ on $A^*$,…