In this paper we prove the Schur-Weyl duality between the symplectic group and the Brauer algebra over an arbitrary infinite field K. We show that the natural homomorphism from the Brauer algebra Bn(−2m) to the endomorphism algebra of the tensor space (K2m)⊗n as a module over the symplectic similitude group GSp2m(K) (or equivalently, as a module over the symplectic group Sp2m(K)) is always surj...

There is a close relationship between Mumford’s geometric invariant theory (GIT) in (complex) algebraic geometry and the process of reduction in symplectic geometry. GIT was developed to construct quotients of algebraic varieties by reductive group actions and thus to construct and study moduli spaces [28, 29]. When a moduli space (or a compactification of a moduli space) over C can be construc...

We give two constructions of surfaces in simply-connected 4-manifolds with non simply-connected complements. One is an iteration of the twisted rim surgery introduced by the first author [7]. We also construct, for any group G satisfying some simple conditions, a simply-connected symplectic manifold containing a symplectic surface whose complement has fundamental group G. In each case, we produ...

In this paper we give an explicit construction of a symplectic Lefschetz fibration whose total space is a smooth compact four dimensional manifold with a prescribed fundamental group. We also study the numerical properties of the sections in symplectic Lefschetz fibrations and their relation to the structure of the monodromy group. Partially supported by DGYCYT grant PB96-0234 Partially support...

In this thesis, we introduce the odd dimensional symplectic manifolds. In the first half we study the Hodge theory on the basic symplectic manifolds. We can define two cohomology theories on them, the standard basic de Rham cohomology gheory and a basic version of the Koszul-Brylinski-Mathieu 'harmonic' symplectic cohomology theory. Among our main results are a collection of examples for which ...

This paper gives methods for understanding invariants of symplectic quotients. The symplectic quotients that we consider are compact symplectic manifolds (or more generally orbifolds), which arise as the symplectic quotients of a symplectic manifold by a compact torus. A companion paper [23] examines symplectic quotients by a nonabelian group, showing how to reduce to the maximal torus. Through...

We prove that every RAAG (Right Angled Artin Group) embeds in the group of Hamiltonian symplectomorphisms of every symplectic manifold.

In this paper, we construct a quantization functor, associating a complex vector space H(V ) to a finite dimensional symplectic vector space V over a finite field of odd characteristic. As a result, we obtain a canonical model for the Weil representation of the symplectic group Sp (V ). The main new technical result is a proof of a stronger form of the Stone-von Neumann property for the Heisenb...

In this paper, we will study compatible triples on Lie algebroids. Using a suitable decomposition for a Lie algebroid, we construct an integrable generalized distribution on the base manifold. As a result, the symplectic form on the Lie algebroid induces a symplectic form on each integral submanifold of the distribution. The induced Poisson structure on the base manifold can be represented by m...

The spectral metric, defined by Schwarz and Oh using Floertheoretical method, is a bi-invariant metric on the Hamiltonian diffeomorphism group. We show in this note that for certain symplectic manifolds, this metric can not be extended to a bi-invariant metric on the full group of symplectomorphisms. We also study the bounded isometry conjecture of Lalonde and Polterovich in the context of the ...