关于实Jacobi群的表示

给定一个实Jacobi群G,我们考虑G的一个Hilbert空间连续表示的范畴,和G的一个Frechet空间光滑表示的范畴．由Mackey理论,它们分别等价于某个实约化群三的两个表示范畴．在这些范畴等价下,我们证明G,表示的光滑化函子和三一表示的光滑化函子是相容的．利用Casselman—Wallach的实约化群光滑表示理论,我们对G的一类光滑表示定义了广义的矩阵系数．为了证明Fourier—Jacobi模型的重数一定理,我们还提出了实Jacobi群的Gelfand—Kazhdan判别法．     

实Lie超代数的有限维实不可约表示

<正> 本文主要是将有限维实Lie超代数的有限维实不可约表示的分类归结为有限维复Lie超代数的有限维复不可约表示的分类问题(为了简单,以下将“有限维”字样统统略去).由于复的可解与单纯Lie超代数的不可约表示是已知的,从而复的可解与单纯     

正则的正实部函数的导数估计

讨论了正则的正实部函数的导数估计问题,利用正实部函数的性质,得到三阶导数、四阶导数的准确估计式.     

关于对称共轭点的有界正实部亚纯星象函数类

引入了一类关于对称共轭点的有界正实部亚纯p叶星象函数类,并获得了函数类的积分表达式,充分条件,Fekete-Szeg?问题和卷积性质.特别地,得到了亚纯p叶函数类的另一种积分表示方法.     

实半单Lie代数实不可约表示的分类方法

本文主要利用Satake图和表示的首权,简单而明确地给出了实半单Lie代数g的表示相关性的充要条件和自相关表示容许第一类型反对合的充要条件。 文献[1]中还指出,利用本方法计算出g的复不可约表示为实表示复化的条件,修订了文献[2]中关于D_2m^2m的第2m-1个基本表示以及文献[5]中关于E₆⁽¹⁾与E₆⁽¹⁾的论断的疏忽之处。     

矩阵具有正实部特征值的判定

利用根与系数的关系.证明了特征方程没有零实部根的充要条件,给出了矩阵特征值至少具有一个正实部的充分条件,最后通过示例计算验证了该方法的有效性.     

实酉群表示的限制问题

本文介绍实酉群表示限制问题的一些新进展.特别地,我们简单说明实酉群Gan-Gross-Prasad猜想的证明思路.     

分裂四元数的实表示矩阵的棣莫弗定理

依据分裂四元数的概念,首先,给出了分裂四元数的实表示矩阵形式,将对分裂四元数的研究转化为实数域上四阶矩阵的研究;其次,根据分裂四元数不同的极表示形式,得到了分裂四元数实表示矩阵相应的棣莫弗定理,推广了欧拉公式,并给出了单位分裂四元数的实表示矩阵方程的求根公式.最后,通过算例验证了结论的正确性.     

实Banach代数的表示

本文研究了对任意厄米实Banach*-代数的表示理论进行系统研究. 利用对该类代数所定义的一般态空间展开讨论. 获得了该类代数上可表示泛函的一系列好的性质,进而给出了不可约表示的等价刻画.这些结果将Naimark、Gaur等人的工作进行了推广.     

一四元数矩阵方程组的实部半正定解

设Ａ是一个ｎ阶实四元数方阵，若对任意的非零ｎ元列向量ｘ，有ｘＡｘ的实部非负，则称Ａ是一个实部半正定阵，本文给出了实四元数矩阵方程组。     

The Topology of the Real Part of a Holomorphic Function

We describe the connection between the Milnor fibre of a holomorphic function and the Milnor fibre of its real part and we derive some simple equations for manifolds appearing as real links of real parts of holomorphic functions.     

Real hypersurfaces with constant principal curvatures in the complex hyperbolic plane

We classify real hypersurfaces with constant principal curvatures in the complex hyperbolic plane. It follows from this classification that all of them are open parts of homogeneous ones.

     

Mazur's Principle for Totally Real Fields of Odd Degree

In this paper, we prove an analogue of the result known as Mazur's Principle concerning optimal levels of mod Galois representations. The paper is divided into two parts. We begin with the study (following Katz–Mazur) of the integral model for certain Shimura curves and the structure of the special fibre. It is this study which allows us to generalise, in the second part of this paper, Mazur's result to totally real fields of odd degree.     

Real GM-biquadrics

We consider real algebraic varieties that are the intersection of two real quadrics. For brevity, we refer to such varieties as real biquadrics. The rigid isotopy classes of real biquadrics have been described long ago. In the present paper, we find the rigid isotopy classes in which the biquadrics are GM-varieties.     

Real hypersurfaces in complex space forms concerned with the local symmetry

This paper consists of two parts. In the first, we find some geometric conditions derived from the local symmetry of the inverse image by the Hopf fibration of a real hypersurface M in complex space form M _m(4ε). In the second, we give a complete classification of real hypersurfaces in M _m(4ε) which satisfy the above geometric facts. The second author was supported by DGICYT research project BFM 2001-2871-C04-01 and the first and the third authors were supported by grant Proj. No. R14-2002-003-01001-0 from Korea Research Foundation, Korea 2006.     

Geometry of Truncated Symmetric Products and Real Roots of Real Polynomials

We study the conditions for truncated symmetric products ofmanifolds to be manifolds. In particular, we show that suitablydefined spaces of systems of real roots of real polynomialsare homeomorphic to real projective spaces. 1991 MathematicsSubject Classification 57N99, 26C10.     

实循环矩阵与实对角矩阵相似问题

本文中我们证明了与实对角矩阵相似的每一个实循环矩阵都是对称的．并给出了一个正交变换，使得任意的ｎ×ｎ实循环对称矩阵通过该变换与实对角矩阵相似．     

Real dicompact textures

A notion of real compactness for completely biregular bi-T₂ ditopological texture spaces is defined and studied under the name real dicompactness. In particular it is shown that real dicompact spaces are nearly plain ∗-spaces, and an important characterization is presented. Finally the connection of this work with topological and bitopological real compactness is discussed in a categorical setting.     

Real Closed Valuation Rings

The real closed valuation rings, i.e., convex subrings of real closed fields, form a proper subclass of the class of real closed domains. It is shown how one can recognize whether a real closed domain is a valuation ring. This leads to a characterization of the totally ordered domains whose real closure is a valuation ring. Real closures of totally ordered factor rings of coordinate rings of real algebraic varieties are very frequently valuation rings. In particular, the real closure of the coordinate ring of a curve is an SV-ring (i.e., the factor rings modulo prime ideals are valuation rings). Real closed valuation rings play a role in the definition of real closed rings, as well as in the construction of real closures of rings and porings. They can also be used for the study of univariate differentiable semi-algebraic functions. This leads to the notion of differentiablility of semi-algebraic functions along half branches of curves.