Related papers: Intersection pairings in the N-fold reduced produc…

We compute the symplectic volume of the symplectic reduced space of the product of N coadjoint orbits of a compact connected Lie group G. We compare our result with the result of Suzuki and Takakura , who study this in the case G = SU(3)…

We provided two explicit formulas for the intersection cohomology (as a graded vector space with pairing) of the symplectic quotient by a circle in terms of the $S^1$ equivariant cohomology of the original symplectic manifold and the fixed…

We give various realizations of the adjoint orbits of a semi-simple Lie group and describe their symplectic geometry. We then use these realizations to identify a family of Lagrangean submanifolds of the orbits.

In this paper we prove a residue formula for intersection pairings of reduced spaces of certain quasi-Hamiltonian G-spaces, by constructing the corresponding Hamiltonian G-space. Our argument closely follows the methods of a 1998 paper of…

Let M be the product of two compact Hamiltonian T-spaces X and Y. We present a formula for evaluating integrals on the symplectic reduction of M by the diagonal T action. At every regular value of the moment map for X x Y, the integral is…

In this survey article, we describe imploded cross-sections, which were developed in order to solve the problem that the cross-section of a Hamiltonian $K$-space is usually not symplectic. In some specific examples we contrast the…

We compute the equivariant local index for the reduced space in a symplectic cut space, provided that the reduced space is compact.

We study the general geometrical structure of the coadjoint orbits of a semidirect product formed by a Lie group and a representation of this group on a vector space. The use of symplectic induction methods gives new insight into the…

We use cotangent bundles of spaces of smooth embeddings to construct symplectic dual pairs involving the group of volume preserving diffeomorphisms. Via symplectic reduction we obtain descriptions of coadjoint orbits of this group in terms…

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,…

The result contained in this paper is an application of a fixed point formula associated with Hamiltonian loop group action. We obtain a G-space which is a geometric dual of the Verlinde's fusion product. Also we obtain a proof of Verlinde…

We consider two natural Lagrangian intersection problems in the context of symplectic toric manifolds: displaceability of torus orbits and of a torus orbit with the real part of the toric manifold. Our remarks address the fact that one can…

In this article we give formulas for the Riemann-Roch number of a symplectic quotient arising as the reduced space corresponding to a coadjoint orbit (for an orbit close to 0) as an evaluation of cohomology classes over the reduced space at…

This paper presents a proof of the existence of standard symplectic coordinates near a set of smooth, orthogonally intersecting symplectic submanifolds. It is a generalization of the standard symplectic neighborhood theorem. Moreover, in…

For two oriented simple closed curves on a compact orientable surface with a connected boundary we introduce a simple computation of a value in the first homology group of the surface, which detects in some cases that the geometric…

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…

We study the orbit structure and the geometric quantization of a pair of mutually commuting hamiltonian actions on a symplectic manifold. If the pair of actions fulfils a symplectic Howe condition, we show that there is a canonical…

We compute the intersection multiplicities of special cycles in Lubin-Tate spaces, and formulate a new arithmetic fundamental lemma relating these intersections to derivatives of orbital integrals.

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…

We describe the admissible coadjoint orbits of a compact connected Lie group and their spin-c quantization.