相关论文: On the geometry of nilpotent orbits
The equations of motion for $N$ non-relativistic particles attracting according to Newton's law are shown to correspond to the equations for null geodesics in a $(3N+2)$-dimensional Lorentzian, Ricci-flat, spacetime with a covariantly…
We reveal a correspondence between the homological torsion of the Bianchi groups and new geometric invariants, which are effectively computable thanks to their action on hyperbolic space. We use it to explicitly compute their integral group…
Let $\overline{B}$ be a smooth projective varieity, and $Z \subset \overline{B}$ a simple normal crossing divisor. Assume that $B = \overline{B} - Z$ admits a variation of pure, polarized Hodge structure. The divisor $Z$ is naturally…
We describe basic concepts of noncommutative geometry and a general construction extending the familiar duality between ordinary spaces and commutative algebras to a duality between Quotient spaces and Noncommutative algebras. Basic tools…
Let G be a (real or complex) linear reductive algebraic group acting on an affine variety V. Let W be a subvariety. In this work we study how the G-orbits intersect W. We develop a criterion to determine when the intersection can be…
The properties of LRS class II perfect fluid space-times are analyzed using the description of geometries in terms of the Riemann tensor and a finite number of its covariant derivatives. In this manner it is straightforward to obtain the…
We obtain the Seiberg-Witten geometry for four-dimensional N=2 gauge theory with gauge group SO(2N_c) (N_c \leq 5) with massive spinor and vector hypermultiplets by considering the gauge symmetry breaking in the N=2 $E_6$ theory with…
The main result of this paper is a new parameterization of the orbits of a symmetric subgroup on a partial flag variety. The parameterization is in terms of certain Spaltenstein varieties, on one hand, and certain nilpotent orbits, on the…
In the case of complex symplectic and orthogonal groups, we find $(\mathfrak{g}, K)-$modules with the property that their $K-$structure matches the structure of regular functions on the closures of nilpotent orbits. This establishes a…
We generalize the coset procedure of homogeneous spacetimes in (pseudo-)Riemannian geometry to non-Lorentzian geometries. These are manifolds endowed with nowhere vanishing invertible vielbeins that transform under local non-Lorentzian…
The Hilbert manifold $\Sigma$ consisting of positive invertible (unitized) Hilbert-Schmidt operators has a rich structure and geometry. The geometry of unitary orbits $\Omega\subset \Sigma$ is studied from the topological and metric…
The \lq\lq effective geometry" formalism is used to study the perturbations of a perfect barotropic Newtonian self-gravitating rotating and compressible fluid coupled with gravitational backreaction. The case of a uniformly rotating…
Given a compact Riemannian manifold together with a group of isometries, we discuss MCF of the orbits and some applications: eg, finding minimal orbits. We then specialize to Lagrangian orbits in Kaehler manifolds. In particular, in the…
In this paper we analyse Abelian diagonal orthogonally transitive spacetimes with spacelike orbits for which the matter content is a stiff perfect fluid. The Einstein equations are cast in a suitable form for determining their geodesic…
The formalism of nilpotent mechanics is introduced in the Lagrangian and Hamiltonian form. Systems are described using nilpotent, commuting coordinates $\eta$. Necessary geometrical notions and elements of generalized differential…
Moduli spaces of a large set of $3d$ $\mathcal{N}=4$ effective gauge theories are known to be closures of nilpotent orbits. This set of theories has recently acquired a special status, due to Namikawa's theorem. As a consequence of this…
The "Seifert Conjecture" asks, "Does every non-singular vector field on the 3-sphere ${\mathbb S}^3$ have a periodic orbit?" In a celebrated work, Krystyna Kuperberg gave a construction of a smooth aperiodic vector field on a plug, which is…
In recent years, the finite W-algebras associated to a semisimple Lie algebra and its nilpotent element have been studied intensively from different viewpoints. In this lecture series, we shall present some basic constructions, connections,…
In this paper, we shall prove that any two (projective) symplectic resolutions of a nilpotent orbit closure in a classical simple Lie algebra are connected by a finite sequence of diagrams which are locally trivial families of Mukai flops…
Arnold pointed out that the Euler equation of incompressible ideal hydrodynamics describes geodesics on the group of volume-preserving diffeomorphisms. A simple analogue is the Euler equation for a rigid body, which is the geodesic equation…