相关论文: The Szego kernel of a symplectic quotient

For a compact CR manifold $(X,T^{1,0}X)$ of dimension $2n+1$, $n\geq 2$, admitting a $S^1\times T^d$ action, if the lattice point $(-p_1,\cdots,-p_d)\in\mathbb{Z}^{d}$ is a regular value of the associate CR moment map $\mu$, then we…

The symplectic group Sp(2g,Z) is a subgroup of the linear group SL(2g,Z) and admits a faithful action on the sphere S^(2g-1), induced from its linear action on Euclidean space R^(2g). Generalizing corresponding results for linear groups, we…

Let $M$ be a symplectic manifold, equipped with a Hamiltonian action of a torus $T$. We give an explicit formula for the rational cohomology ring of the symplectic quotient $M//T$ in terms of the cohomology ring of $M$ and fixed point data.…

The Berezin quantization on a simply connected homogeneous K\"{a}hler manifold, which is considered as a phase space for a dynamical system, enables a description of the quantal system in a (finite-dimensional) Hilbert space of holomorphic…

Given a compact symplectic manifold $(M,\omega)$ and a compact Lagrangian submanifold $L\subset(M,\omega)$, we describe small deformations of the pair $(\omega,L)$ modulo the action by isotopies. We show that the resulting moduli space can…

We address the problem of computing the fundamental group of a symplectic $S^1$-manifold for non-Hamiltonian actions on compact manifolds, and for Hamiltonian actions on non-compact manifolds with a proper moment map. We generalize known…

Let $M$ be a relatively compact connected open subset with smooth connected boundary of a complex manifold $M'$. Let $(L,h^L)\rightarrow M'$ be a positive line bundle over $M'$. Suppose that $M'$ admits a holomorphic $\mathbb{R}$-action…

Given a Lie group G, a G-manifold M, and a point b of M with compact stabilizer, we construct slices for the lifted tangent and cotangent actions at a pre-image of b in terms of a slice for the G-action on M at the point b. We interpret the…

Let M be a symplectic manifold equipped with a Hamiltonian circle action and let L be an invariant Lagrangian submanifold of M. We study the problem of counting holomorphic disc sections of the trivial M-bundle over a disc with boundary in…

All factorizable Lie bialgebra structures on complex reductive Lie algebras were described by Belavin and Drinfeld. We classify the symplectic leaves of the full class of corresponding connected Poisson-Lie groups. A formula for their…

We study the cohomology rings of snc log symplectic pairs $(X,Y)$ which have log symplectic forms of pure weight. We show that under a certain natural condition, the cohomology ring of $X \setminus Y$ exhibits the curious hard Lefschetz…

The maximal complexifications adapted to the Levi Civita connection for a distinguished one-parameter family of left-invariant metrics on a real semisimple Lie group G are determined. For G = SL(2,R) their realizations as invariant Riemann…

Let $(M,\omega_M)$ be a six dimensional closed monotone symplectic manifold admitting an effective semifree Hamiltonian $S^1$-action. We show that if the minimal (or maximal) fixed component of the action is an isolated point, then…

Let $K\to U(V)$ be a unitary representation of the compact Lie group $K$. Then there is a canonical moment mapping $\rho\colon V\to\mathfrak k^*$. We have the Koszul complex ${\mathcal K}(\rho,\mathcal C^\infty(V))$ of the component…

In this paper, we develop results in the direction of an analogue of Sjamaar and Lerman's singular reduction of Hamiltonian symplectic manifolds in the context of reduction of Hamiltonian generalized complex manifolds (in the sense of Lin…

In this paper, we begin a quantization program for nilpotent orbits of a real semisimple Lie group. These orbits and their covers generalize the symplectic vector space. A complex structure polarizing the orbit and invariant under a maximal…

On an asymptotically conic manifold $(M,g)$, we analyze the asymptotics of the integral kernel of the resolvent $R_q(k):=(\Delta_q+k^2)^{-1}$ of the Hodge Laplacian $\Delta_q$ on $q$-forms as the spectral parameter $k$ approaches zero,…

Let $M$ be complex projective manifold, and $A$ a positive line bundle on it. Assume that $SU(2)$ acts on $M$ in a Hamiltonian manner, with nowhere vanishing moment map, and that this action linearizes to $A$. Then there is an associated…

We consider actions of reductive complex Lie groups $G=K^C$ on K\"ahler manifolds $X$ such that the $K$--action is Hamiltonian and prove then that the closures of the $G$--orbits are complex-analytic in $X$. This is used to characterize…

Let H be the 15- dimensional connected semisimple Lie group with its Iwasawa decomposition of H. Let G be the group of the semi direct product of H and the four dimensional real vector group . The goal of this paper is to define the Fourier…