相关论文: On the cell structure of flag manifolds
The purpose of this paper is to describe certain natural 4-vector fields on quaternionic flag manifolds, which geometrically determine the Bruhat cell decomposition. This structure naturally descends from the symplectic group, where it is…
We define flag structures on a real three manifold M as the choice of two complex lines on the complexified tangent space at each point of M. We suppose that the plane field defined by the complex lines is a contact plane and construct an…
A class of Cantor-type spaces and related geometric structures are discussed.
In the first part of this paper we study geometric formality for generalized flag manifolds, including full flag manifolds of exceptional Lie groups. In the second part we deal with the problem of the classification of invariant almost…
Flag manifolds are shown to describe the relations between configurations of distinguished points (topologically equivalent to punctures) embedded in a general spacetime manifold. Grassmannians are flag manifolds with just two subsets of…
For a complex semi-simple group G and its real form G0 we define a Poisson structure on the flag variety of G such that all the Bruhat cells (for a suitable choice of a Borel subgroup of G) as well as all the G0-orbits are Poisson…
We describe moduli spaces of invariant generalized complex structures and moduli spaces of invariant generalized K\"ahler structures on maximal flag manifolds under $B$-transformations. We give an alternative description of the moduli space…
This article describes a natural piecewise Euclidean bi-simplicial cell structure for the space of $n$-element multisets in a fixed Euclidean rectangle. In particular, we highlight some connections with spaces of complex polynomials and…
We introduce a formalism for the geometry of eukaryotic cells and organisms.Cells are taken to be star-convex with good biological reason. This allows for a convenient description of their extent in space as well as all manner of cell…
The purpose of this note is to define tri-moment maps for certain manifolds that carry closed non-degenerate 4-forms and an $Sp(1)^n$-action. Examples include quaternionic vector spaces and flag manifolds. We show how this map can be used…
In the first part of this work, we study Dirichlet-Voronoi domains for discrete isometry groups of Riemannian manifolds, in view of constructing cell structures on homogeneous (complete, real) flag manifolds, equivariant with respect to the…
A cell algebra structure is found for a family of generalized Schur algebras previously studied by the author. This cell algebra structure is then used to construct the irreducible representations of these algebras and to determine when the…
This paper defines for each object $X$ that can be constructed out of a finite number of vertices and cells a vector $fX$ lying in a finite dimensional vector space. This is the flag vector of $X$. It is hoped that the quantum topological…
The notion of a quaternionic gerbe is presented as a new way of bundling algebraic structures over a four manifold. The structure groupoid of this fibration is described in some detail. The Euclidean conformal group R*SO(4) appears…
The nonnegative Grassmannian is a cell complex with rich geometric, algebraic, and combinatorial structures. Its study involves interesting combinatorial objects, such as positroids and plabic graphs. Remarkably, the same combinatorial…
For any semifield K we define a K-form of a partial flag manifold of a semisimple group G of simply laced type over the complex numbers. The definition is in terms of the theory of canonical bases.
In this work we study the existence of invariant almost complex structures on real flag manifolds associated to split real forms of complex simple Lie algebras. We show that, contrary to the complex case where the invariant almost complex…
Many interesting geometric structures can be described as regular infinitesimal flag structures, which occur as the underlying structures of parabolic geometries. Among these structures we have for instance conformal structures, contact…
It is well known that for many semilinear parabolic equations there is a global attractor which has a cell complex structure with finite dimensional cells. Additionally, many semilinear parabolic equations have equilibria with finite…
We define complex Minkowski superspace in 4 dimensions as the big cell inside a complex flag supermanifold. The complex conformal supergroup acts naturally on this super flag, allowing us to interpret it as the conformal compactification of…