An Adjacency Criterion for Coxeter Matroids

A Coxeter matroid is a generalization of matroid, ordinary matroid being the case corresponding to the family of Coxeter groups A _n , which are isomorphic to the symmetric groups. A basic result in the subject is a geometric characterization of Coxeter matroid in terms of the matroid polytope, a result first stated by Gelfand and Serganova. This paper concerns properties of the matroid polytope. In particular, a criterion is given for adjacency of vertices in the matroid polytope.     

On the Classification of Flag-Transitive c.c*- Geometries

Let ( G) be a flag-transitive c.c*-geometry whose point-stabilizer is not an affine group. We list all known examples and show that, if (, G) is a minimal unknown example, then G is an almost simple group and the commutator subgroup G is a simple group of Lie type.     

Homotopy of Non-Modular Partitions and the Whitehouse Module

We present a class of subposets of the partition lattice _n with the following property: The order complex is homotopy equivalent to the order complex of _n – 1, and the S _n -module structure of the homology coincides with a recently discovered lifting of the S _n – 1-action on the homology of _n – 1. This is the Whitehouse representation on Robinson's space of fully-grown trees, and has also appeared in work of Getzler and Kapranov, Mathieu, Hanlon and Stanley, and Babson et al.One example is the subposet P _n ⁿ – 1 of the lattice of set partitions _n , obtained by removing all elements with a unique nontrivial block. More generally, for 2 k n – 1, let Q _n ^k denote the subposet of the partition lattice _n obtained by removing all elements with a unique nontrivial block of size equal to k, and let P _n ^k = _{i = 2} ^k Q _n ⁱ . We show that P _n ^k is Cohen-Macaulay, and that P _n ^k and Q _n ^k are both homotopy equivalent to a wedge of spheres of dimension (n – 4), with Betti number . The posets Q _n ^k are neither shellable nor Cohen-Macaulay. We show that the S _n -module structure of the homology generalises the Whitehouse module in a simple way.We also present a short proof of the well-known result that rank-selection in a poset preserves the Cohen-Macaulay property.     

Wavelets in Banach Spaces

We describe a construction of wavelets (coherent states) in Banach spaces generated by admissible group representations. Our main targets are applications in pure mathematics while connections with quantum mechanics are mentioned. As an example, we consider operator-valued Segal–Bargmann-type spaces and the Weyl functional calculus.     

Four-Dimensional Compact Projective Planes with a Solvable Collineation Group

We consider a four-dimensional compact projective plane whose collineation group is six-dimensional and solvable with a nilradical N isomorphic to Nil×R, where Nil denotes the three-dimensional, simply connected, non-Abelian, nilpotent Lie group. We assume that fixes a flag p W, acts transitively on and fixes no point in the set W\p. Under these conditions, we will prove that either contains a three-dimensional group of elations or acts doubly transitively on .     

二步幂零李群上—类左不变微分算子亚椭圆的充要条件

本文我们用幂零李群表示的方法,给出了二步幂零李群上一类左不变微分算子是亚椭圆的充要条件．     

企业集团资本增值域的选择与优化

企业集团是资本的集合体,它在资本本质的推动下,不断寻求资本增值的最大化。但是我国企业集团由于受经济体制转换期的影响,以及自身经验的不足,未能正确定位集团的发展领域,从而未能实现资本的增值。文章根据我国企业集团当前存在的问题,结合项目实践中的体会,讨论了如何正确认识资本增值域,以及如何正确选择与优化资本增值域     

某些幂零子群与可解性

本文利用某些幂子群的半正规性,讨论有限群的可解性,所得结果统一推广了王品超、赵耀庆的若干结果。     

K-Theory for the Integer Heisenberg Groups

We give a closed formula for topological K-theory of the homogeneous space N/, where is the standard integer lattice in the simply connected Heisenberg Lie group N of dimension 2n+1, n . The main tools in our calculations are obtained by computing diagonal forms for certain incidence matrices that arise naturally in combinatorics.