秩2紧致单纯李群的不可约表示(III)

本文应用前两篇文章（I）,（II）所采用的方法讨论了B₂,G₂群的不可约表示,给出了求B₂,G₂群不可约表示的方法并给出了它们的一些低维的不可约表示。     

阶化李代数SU(m/n)的不可约表示

本文利用李代数SU(n)不可约张量的概念,给出求阶化李代数SU(m/n)不可约表示的方法。并且给出SU(3/2)和SU(m/n)若干较简单的不可约表示例子。     

SPL(2，1)超代数的不可分解表示和不可约表示

利用ＳＰＬ（２,１）的非齐次玻色 费米实现,研究了ＳＰＬ（２,１）在Ｈｅｉｓｅｎｂｅｒｇ Ｗｅｙｌ超代数的广义包络代数的子空间和商空间上的不可分解表示和不可约表示,并给出了它的全部有限维不可约表示 关键词：     

空间羣不可约表示对称冪及反对称冪的简约

本文将作者们对空间羣不可约表示直接乘积的简约所发展的方法推广到空间羣不可约表示对称幂及反对称幂的简约,列出了对六角密积与纤维锌矿结构对称化平方的计算结果;利用这些结果,对组态不隐定性作了初步讨论。     

SU_3群的多项式基底及其Clebsch-Gordan系数的明显表达式

利用对称性与Young图在多项式空间上构成了SU_n群的不可约表示及积表示的完全基底,从而不但区分了非单纯权也区分了积表示的非简单可约性,并在此基础上用构成不变量法得到SU_3群的Clebsch-Gordan系数的明显表达式     

李超代数B(0,1)的非齐次微分实现,Boson-Fermion实现及其表示

本文研究了李超代数B(0,1)在非齐次多项式空间上的微分实现(称为非齐次微分实现),和对应的非齐次Boson—Fermion实现.利用非齐次Boson-Fermion实现,在Heisenberg-Weyl超代数的通用包络代数,其子空间和商空间上研究了B(0,1)的一类新的不可分解表示和不可约表示.B(0,1)的所有有限维不可约表示则作为特殊情况全部给出.     

李超代数B(0,1)的非齐次微分实现,Boson-Fermion实现及其表示

本文研究了李超代数B(0,1)在非齐次多项式空间上的微分实现(称为非齐次微分实现),和对应的非齐次Boson-Fermion实现.利用非齐次Boson-Fermion实现,在 Heisenberg-Weyl超代数的通用包络代数,其子空间和商空间上研究了B(0,1)的一类新的不可分解表示和不可约表示.B(0,1)的所有有限维不可约表示则作为特殊情况全部给出.     

PrP_5O_(14)晶体中Pr~(3 )离子的晶场参数和能级

本文在C_(2v)群近似下,以点群的不可约表示基矢为波函数,计算了PrP_5O_(14)晶体中Pr~(3 )的晶场参数,Racah参数,组态相互作用参数,自旋-轨道相互作用参数.计算中考虑了J混淆和J不混淆两种情况.计算了J混淆情况的能级,并指派了不可约表示,计算和实验能级符合较好.     

利用双参变形自旋相干态计算量子代数SU(2)q,s的Clebsch-Gordan系数

利用量子代数SU(2)_q,s的双参数变形自旋相干态,通过引入量子代数SU(2)_q,s的不可约表示张量积空间的Bargmann表示,导出了这一表示中不可约表示基底、双参数变形自旋相干态以及算符的表达式.最后导出了量子代数SU(2)_q,s在双参数变形自旋相干态下的Clebsch－Gordan系数.     

单纯李群的不可约表示(I)——单纯经典李群无穷小生成元的张量基

在本文中,通过对单纯经典李群无穷小生成元对易关系的分析,引入了无穷小生成元的一组新基——张量基。在张量基中,无穷小生成元可以写为若干个相互对易的标量,若干组相互对易的角动量;若干组不可约张量。它们满足的对易关系简单而有规律。利用单纯经典李群无穷小生成元的张量基及前几篇文章“秩2紧致单纯李群的不可约表示I,II,III”中所用的方法,我们就可以系统地解决单纯经典李群的不可约表示问题。     

黑克、布劳、及伯曼-温采尔代数的诱导及分导系数和量子经典李代数的耦合与重新耦合系数

本文总结了计算黑克、布劳、及伯曼 温采尔代数在各种工数链下诱导及分导系数的线性方程方法(LEM)。特别强调了关于A,B,C,D型李代数及其量子情形与其中心代数之间的舒尔 魏尔 布劳双关性关系。这一关系使我们能够利用相应中心代数的诱导及分导系数计算出经典李代数及其量子情形的耦合与重新耦合系数。讨论了从该方法得到B,C,D型李代数不可约表示克罗内克积分解的应用。基于LEM还得到了处理对应于置换群CG系列问题的黑克代数张量积的方法。     

Unitary representations of the Virasoro and super-Virasoro algebras

It is shown that a method previously given for constructing representations of the Virasoro algebra out of representations of affine Kac-Moody algebras yields the full discrete series of highest weight irreducible representations of the Virasoro algebra. The corresponding method for the super-Virasoro algebras (i.e. the Neveu-Schwarz and Ramond algebras) is described in detail and shown to yield the full discrete series of irreducible highest weight representations.     

Non-planar operator mixing by Brauer representations

We study the action of the dilatation operator on the basis of local operators constructed from elements of the walled Brauer algebra, with non-planar corrections fully taken into account. We will see that the operator mixing can be neatly expressed in terms of the irreducible representations of the algebra. In particular we focus on a role of the integer that determines the number of boxes in the representations.     

Superfields as Representations

We study irreducible and reducible representations of the generalized Lie algebra of Wess and Zumino. The algebra is integrated to a group with the help of Grassmann algebras and the representations of the algebra are made into representations of the group. We construct invariant sesquilinear forms that are positive definite for the Wess-Zumino algebra over the complex field. We define irreducible superfields for any spin J as specific realizations of such representations. All superfields appearing in the literature are either equivalent to one of these or built up out of these superfields.     

Structure constants of algebras of projective representations of point groups

Structure constants (MIRREPS) of algebras of characters of irreducible projective representations of all three-dimensional point groups are listed. Possible applications of the MIRREPS are indicated.     

On the structure of unitary conformal field theory II: Representation theoretic approach

Two-dimensional, unitary rational conformal field theory is studied from the point of view of the representation theory of chiral algebras. Chiral algebras are equipped with a family of co-multiplications which serve to define tensor product representations. Chiral vertices arise as Clebsch-Gordan operators from tensor product representations to irreducible subrepresentations of a chiral algebra. The algebra of chiral vertices is studied and shown to give rise to representations of the braid groups determined by Yang-Baxter (braid) matrices. Chiral fusion is analyzed. It is shown that the braid- and fusion matrices determine invariants of knots and links. Connections between the representation theories of chiral algebras and of quantum groups are sketched. Finally, it is shown how the local fields of a conformal field theory can be reconstructed from the chiral vertices of two chiral algebras.     

Tensor Products of Hecke Algebras

Tensor product of irreducible representations of Hecke algebras are discussed. It is found that the tensor product of irreps of Hecke algebras generates representations of Birman-Wenzl algebra C_ƒ(γ, q) with γ = q³ or-q^-3. A procedure for the evaluation of tensor product coefficients (TPC's) of H_ƒ (q)oH_ƒ(q) ↓ C_ƒ(γ,q) is established when the representations of Cƒ(γ, q) remain irreducible. An example of deriving TPC's of H_ƒ (q)oH_ƒ(q) ↓ C_ƒ(γ, q) is given. It is also found that indecomposable representation of C₄(γ q) occurs in the tensor product [211]o[31].     

A Weyl group for the Virasoro andN=1 super-Virasoro algebras

We introduce a Weyl group for the highest weight modules over the Virasoro algebra and the Neveu-Schwarz and Ramond superalgebras. Using this group we rewrite the character formulae for the irreducible highest weight modules over these algebras in the form of the classical Weyl character formula for the finite-dimensional irreducible representations of semi-simple Lie algebras (and also of the Weyl-Kac character formula for the integrable highest weight modules over affine Kac-Moody algebras). This is the same group we introduced recently in order to rewrite in a similar manner the characters of the singular highest weight modules over the affine Kac-Moody algebraA ₁ ⁽¹⁾ .     

The spectrum of the algebra of skew differential operators and the irreducible representations of the quantum Heisenberg algebra

The left spectrum of a wide class of the algebras of skew differential operators is described. As a sequence, we determine and classify all the algebraically irreducible representations of the quantum Heisenberg algebra over an arbitrary field.