Related papers: A Residue Formula for SU(2)-valued Moment Maps

It is well-known that the intersection multiplicities of Schubert classes in the Grassmanian are Littlewood-Richardson coefficients. We generalize this statement in the context of quiver representations. Here the intersection multiplicity…

A recent analysis of real general relativity based on multisymplectic techniques has shown that boundary terms may occur in the constraint equations, unless some boundary conditions are imposed. This paper studies the corresponding form of…

We introduce geometric quantization in the setting of shifted symplectic structures. We define Lagrangian fibrations and prequantizations of shifted symplectic stacks and their geometric quantization. In addition, we study many examples…

In this article, we give new results in the startpoint theory for quasi-pseudometric spaces. The results we present provide us with the existence of startpoint (endpoint, fixed point) for multi-valued maps defined on a bicomplete…

Volumes of moduli spaces of hyperbolic cone surfaces were previously defined and computed when the angles of the cone singularities are at most 2pi. We propose a general definition of these volumes without restriction on the angles. This…

Let G be a compact connected Lie group, and (M,\omega) a Hamiltonian G-space with proper moment map \mu. We give a surjectivity result which expresses the K-theory of the symplectic quotient M//G in terms of the equivariant K-theory of the…

This article introduces two reduction schemes for Hamiltonian systems on an exact symplectic manifold admitting Lie group symmetries. It is demonstrated that these reduction procedures are equivalent by employing a modified…

We introduce the notion of relative pseudocoefficient for relative discrete series of real spherical homogeneous spaces of reductive groups. We prove that such relative pseudocoefficient does not exist for semisimple symmetric spaces of…

The presence of symmetries in a Hamiltonian system usually implies the existence of conservation laws that are represented mathematically in terms of the dynamical preservation of the level sets of a momentum mapping. The symplectic or…

Let $G$ be a complex simple Lie group, and $\mathfrak{g}$ its Lie algebra. It is well known that a finite-dimensional $G$-module $V$ carrying a nondegenerate invariant bilinear form gives rise to a Hamiltonian Poisson space with a quadratic…

For a finite-dimensional (but possibly noncompact) symplectic manifold with a compact group acting with a proper moment map, we show that the square of the moment map is an equivariantly perfect Morse function in the sense of Kirwan, and…

In this work we discuss some appearances of semi-infinite combinatorics in representation theory. We propose a semi-infinite moment graph theory and we motivate it by considering the (not yet rigorously defined) geometric side of the story.…

This paper aims at providing further studies of the notion of quasi-relative interior for convex sets introduced by Borwein and Lewis. We obtain new formulas for representing quasi-relative interiors of convex graphs of set-valued mappings…

We provide sufficient conditions for two subgroups of a hierarchically hyperbolic group to generate an amalgamated free product over their intersection. The result applies in particular to certain geometric subgroups of mapping class groups…

Given a Hamiltonian system $ (M,\omega, G,\mu) $ where $(M,\omega)$ is a symplectic manifold, $G$ is a compact connected Lie group acting on $(M,\omega)$ with moment map $ \mu:M \rightarrow\mathfrak{g}^{*}$, then one may construct the…

In this paper, we consider surfaces in 4--dimensional pseudo--Riemannian space--forms with index 2. First, we obtain some of geometrical properties of such surfaces considering their relative null space. Then, we get classifications of…

This paper develops the pre-quantization of Lie group-valued moment maps, and establishes its equivalence with the pre-quantization of infinite-dimensional Hamiltonian loop group spaces.

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…

We investigate the covariant Hamiltonian symplectic structure of General Relativity for spatially bounded regions of spacetime with a fixed time-flow vector. For existence of a well-defined Hamiltonian variational principle taking into…

The relative equilibria of a symmetric Hamiltonian dynamical system are the critical points of the so-called augmented Hamiltonian. The underlying geometric structure of the system is used to decompose the critical point equations and…