Related papers: Steinberg slices and group-valued moment maps

Let Phi : M --> g^* be a proper moment map associated to an action of a compact connected Lie group, G, on a connected symplectic manifold, (M,\omega). A collective function is a pullback via \Phi of a smooth function on g^*. In this paper…

We describe smooth compactifications of certain families of reductive homogeneous spaces such as group manifolds for classical Lie groups, or pseudo-Riemannian analogues of real hyperbolic spaces and their complex and quaternionic…

Symplectic reduction is reinterpreted as the composition of arrows in the category of integrable Poisson manifolds, whose arrows are isomorphism classes of dual pairs, with symplectic groupoids as units. Morita equivalence of Poisson…

Any multiplicative quiver variety is endowed with a Poisson structure constructed by Van den Bergh through reduction from a Hamiltonian quasi-Poisson structure. The smooth locus carries a corresponding symplectic form defined by Yamakawa…

Let G be a complex reductive group and K a maximal compact subgroup. If X is a smooth projective G-variety, with a fixed (not necessarily integral) K-invariant Kaehler form, then the K-action is Hamiltonian. Let M be the zero fiber of the…

Symplectic and Poisson structures of certain moduli spaces/Huebschmann,J./ Abstract: Let $\pi$ be the fundamental group of a closed surface and $G$ a Lie group with a biinvariant metric, not necessarily positive definite. It is shown that a…

We generalize in positive characteristics some results of Bien and Brion on log homogeneous compactifications of a homogeneous space under the action of a connected reductive group. We also construct an explicit smooth log homogeneous…

We construct, for each convex polytope, possibly nonrational and nonsimple, a family of compact spaces that are stratified by quasifolds, i.e. each of these spaces is a collection of quasifolds glued together in an suitable way. A quasifold…

We introduce a compactification construction for abstract quasi-local C*-algebras over countable metric spaces equipped with an isometric group action which is functorial with respect to bounded spread isomorphisms. In $1$D, the…

Every topological group $G$ has some natural compactifications which can be a useful tool of studying $G$. We discuss the following constructions: (1) the greatest ambit $S(G)$ is the compactification corresponding to the algebra of all…

For each connected complex reductive group G, we find a family of new examples of complex quasi-Hamiltonian G-spaces with G-valued moment maps. These spaces arise naturally as moduli spaces of (suitably framed) meromorphic connections on…

We consider canonical symplectic structure on the moduli space of flat ${\g}$-connections on a Riemann surface of genus $g$ with $n$ marked points. For ${\g}$ being a semisimple Lie algebra we obtain an explicit efficient formula for this…

The imploded cross-section of a symplectic manifold is a stratified space allowing for an abelianization of its symplectic reduction. After recalling symplectic and Poisson reduction and reviewing the basics of symplectic implosion, we…

These lecture notes explain the construction and basic properties of the wonderful compactification of a complex semisimple group of adjoint type. An appendix discusses the more general case of a semisimple symmetric space.

We investigate Snyder space-time and its generalizations, including Yang and Snyder-de-Sitter spaces, which constitute manifestly Lorenz invariant noncommutative geometries. This work initiates a systematic study of gauge theory on such…

We prove a sharp, quantitative analogue of Helgason's conjecture at the level of distributions: For a semisimple Lie group $G$ of real rank one, Poisson transforms map a Sobolev space on $P\backslash G$ boundedly with closed range to an…

Inspired by the log Gromov-Witten (or GW) theory of Gross-Siebert/Abramovich-Chen, we introduce a geometric notion of log J-holomorphic curve relative to a simple normal crossings symplectic divisor defined in [FMZ1]. Every such moduli…

We consider a connected symplectic manifold $M$ acted on by a connected Lie group $G$ in a Hamiltonian fashion. If $G$ is compact, we prove give an Equivalence Theorem for the symplectic manifolds whose squared moment map $\parallel \mu…

A transitive smooth action of a connected Lie group G on a manifold M is called almost primitive (resp. primitive) if G doesn't contain any proper subgroup (resp. any proper normal subgroup) whose induced action on M is transitive as well.…

The given study uses the methods to identify compactifications of semigroups $S\subset L(X),$ which reside in the space $L(X).$ This method generalizes in some sense the deLeeuw-Glicksberg-Theory to a greater class of functions. The…