辫子群的双参数不可约表示

在广义的Conway条件下,引入双参数完备算符集,借助杨图,给出了B_n群的双参数不可约表示。     

量子代数Uq（C_2）的有限维不可约表示

本文分析了量子代数Ｕｑ（Ｃａ）生成元的对易关系，构造了的秩张量，利用量子代数的张性性质，方便地求出了Ｕｑ（Ｃａ）的有限维不可约表示，部分低维不可的表示被列于表中．     

Birman-Wenzl代数的不可约表示 *

利用诱导表示和线性方程方法构造了Birman-Wenzl代数的不可约表示,并给出了C_f(r,q)当ƒ≤4时的自伴随表示的结果.     

有理样条不可约解的行列式表示

１引言在文［１］中,对于剖分ａ＝ｘ０＜ｘ１＜…＜ｍｎ＝ｂ及给定的ｙ０,ｙ１,…,　…,Ｌ＋Ｍ－１,我们构造了有理样条Ｓ［Ｌ,Ｍ（ｘ）Ｑ［Ｌ,Ｍ］为次数不超过ｍ的多项式全体．在［１］中,已经讨论了Ｓ［Ｌ,Ｍ］（ｘ）的存在性,并指出：若问题（１）（２）（３）可解,则解唯一这里总假设问题（１）（２）（３）可解．２有理样条解不可约的充要条件由Ｓ［Ｌ,Ｍ］（ｘ）的依区间递推算法（见［１］）,我们只需讨论［ｘ０,ｘ１］上的情形．当［Ｘ０,ｘ１］时,将Ｓ［Ｌ,Ｍ］　（ｘ）,Ｐ［Ｌ,Ｍ］　（ｘ）和Ｑ［Ｌ,Ｍ］（…     

一些(双)代数的不可约表示

本文完全刻画了下列代数k,k,k(x,Y,Z|ZX-qXZ=1-θY2,ZY=qYZ,YX= qXY>和M(p,q)=k的不可约表示．     

自由能展开式中点群的不可约表示的基函数

一个群的基函数的选择并非唯一，不同的基函数对应不同的表示矩阵。即使相同的表示矩阵，基函数也可以有不同的选择。在相变的宏观唯象理论中， 自由能展开式可由同一个表示矩阵的基函数来构造，因而给出不可约表示的基函数表就非常有意义。现有文献给出的32点群不可约表示的基函数只写到二次幂，而且有些文献中的同一个不可约表示所选取的不同的基函数却对应不同的表示矩阵，这样在构造群变换不变式时，就会出错。该文将基函数表写至三次幂, 这有助于准确、迅速地写出到六次幂群变换不变的自由能表达式。由新的基函数表发现十八种点群有三次幂的群操作不变式, 高温相属这些点群铁电体, 发生的本征铁电相变为一级相变。     

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．     

恰有二个非线性不可约特征标的有限群

刻划了恰含二个非线性不可纳特征标的有限群，证明了这样的群或为2-群或为3-群或为Frobenius群．     

量子群vq（sl2））的不可约表示

本文引进满足一定关系的六个元素生成的量子群vq(sl(2)),证明了vq(sl(2))具有PBW基且是无零因子环,进而当q不是单根时决定了vq(sl(2))的有限维不可约束表示。     

Braid groups are linear

The braid group can be defined as the mapping class group of the -punctured disk. A group is said to be linear if it admits a faithful representation into a group of matrices over . Recently Daan Krammer has shown that a certain representation of the braid groups is faithful for the case . In this paper, we show that it is faithful for all .

     

Globally Irreducible Representations of Finite Groups and Integral Lattices

The notion of globally irreducible representations of finite groups has been introduced by B. H. Gross, in order to explain new series of Euclidean lattices discovered recently by N. Elkies and T. Shioda using Mordell--Weil lattices of elliptic curves. In this paper we first give a necessary condition for global irreducibility. Then we classify all globally irreducible representations of L ₂(q) and ²B₂(q), and of the majority of the 26 sporadic finite simple groups. We also exhibit one more globally irreducible representation, which is related to the Weil representation of degree (pⁿ-1)/2 of the symplectic group Sp_2n(p) (p 1 (mod 4) is a prime). As a consequence, we get a new series of even unimodular lattices of rank 2(pⁿ–1). A summary of currently known globally irreducible representations is given.     

Linear Representations of the Braid Groups of Some Manifolds

In this paper we prove that the braid group B_n(S²) of 2-sphere, mapping class group M(0,n) of the n-punctured 2-sphere and the braid group B₃(P²) of the projective plane are linear. Partially supported by the Russian Foundation for Basic Research (grant number 02-01-01118).Mathematics Subject Classifications (2000) 20F28, 20F36, 20G35.     

A Family of Complex Irreducible Characters Possessed by Unitary and Special Unitary Groups Defined over Local Rings

Abstract

Let 𝒪 be a discrete valuation ring whose residue field 𝒪/𝔭 is finite and has odd characteristic. Let l be a positive integer. Set R = 𝒪/𝔭 ^l and let R = R[θ] be the ring obtained by adjoining to R a square root of a non-square unit. Consider the involution σ of R that fixes R elementwise and sends θ to ? θ. Let V be a free R-module of rank n > 0 endowed with a non-degenerate hermitian form ( , ) relative to σ. Let U _n (R) be the subgroup of GL(V) that preserves ( , ). Let SU _n (R) be the subgroup of all g ∈ U _n (R) whose determinant is equal to one. Let Ψ be the Weil character of U _n (R).

All irreducible constituents of Ψ are determined. An explicit character formula is given for each of them. In particular, all character degrees are computed. For n > 2 the corresponding results are also obtained for the restriction of Ψ to SU _n (R).     

Quasi-Invariant Measures and Irreducible Representations of the Inductive Limit of Special Linear Groups

Unitary representations of the group are constructed. The construction uses G-quasi-invariant measures on some G-spaces that are subspaces of the space of two-way infinite real matrices. We give a criterion for the irreducibility of these representations.     

Bi-Element Representations of Ternary Groups#

General properties of ternary semigroups and groups are consi-dered. The bi-element representation theory in which every representation matrix corresponds to a pair of elements is built up. Connections with the standard theory are considered and several concrete examples are constructed. For the sake of clarity and completeness the shortened versions of classical Gluskin-Hosszú and Post theorems are also presented.     

On Residual Properties of Pure Braid Groups of Closed Surfaces

We prove that pure braid groups of closed surfaces are almost-direct products of residually torsion free nilpotent groups and hence residually torsion free nilpotent. As a corollary, we prove also that braid groups on 2 strands of closed surfaces are residually nilpotent.     

Braid pictures for Artin groups

We define the braid groups of a two-dimensional orbifold and introduce conventions for drawing braid pictures. We use these to realize the Artin groups associated to the spherical Coxeter diagrams , and and the affine diagrams , , and as subgroups of the braid groups of various simple orbifolds. The cases , , and are new. In each case the Artin group is a normal subgroup with abelian quotient; in all cases except the quotient is finite. We also illustrate the value of our braid calculus by giving a picture-proof of the basic properties of the Garside element of an Artin group of type .