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81.
C.K. Fan 《Journal of Algebraic Combinatorics》1996,5(3):175-189
Let (W, S) be a Coxeter group associated to a Coxeter graph which has no multiple bonds. Let H be the corresponding Hecke Algebra. We define a certain quotient \-H of H and show that it has a basis parametrized by a certain subset W
cof the Coxeter group W. Specifically, W
cconsists of those elements of W all of whose reduced expressions avoid substrings of the form sts where s and t are noncommuting generators in S. We determine which Coxeter groups have finite W
cand compute the cardinality of W
cwhen W is a Weyl group. Finally, we give a combinatorial application (which is related to the number of reduced expressions for w W
cof an exponential formula of Lusztig which utilizes a specialization of a subalgebra of \-H. 相似文献
82.
Janusz Grabowski 《Annals of Global Analysis and Geometry》1993,11(3):213-220
It is proved that for infinite dimensional Lie groups in the sense of the differential calculus of Frölicher and Kriegl the derivative of the exponential mappings is given by the formula d(exp)(X)Y=dexp(X)(e)
0
1
Adexp(–tX)
Y dt, where stands for the left translation ande is the neutral element.This work was supported by the Alexander von Humboldt-Stiftung. 相似文献
83.
84.
85.
提出了一种动力学李代数方法来研究取代苯体系的非线性光学性质. 对于给定的PPP模型(Pariser-Parr-Pople)哈密顿量, 生成了一个动力学李代数. 依据这些代数元构造出演化算子作为群参数的函数, 通过求解一组非线性微分方程能够得到这些群参数. 再按照统计力学中的密度算子公式给出取代苯分子体系偶极矩的统计平均值. 于是导出二阶极化率的表达式. 与其他量子力学计算结果比较, 表明这种动力学李代数方法在预言有机共轭分子的非线性光学性质上同样有用. 相似文献
86.
Xian Zhao Daren Guan Xizhang Yi Guibao Xu Minhua Jiang 《International journal of quantum chemistry》2003,93(5):335-343
A dynamic Lie algebraic (DLA) formulation is applied to the study of nonlinear optical properties of the substituted benzenes. We have described the generation of the dynamic Lie algebra for the model Hamiltonian used in the present study. In terms of these elements of the dynamic algebra we express the evolution operator as a function of the group parameters, which can be determined by means of solving a system of coupled nonlinear differential equations. Thus, in terms of the density matrix operator formalism in statistical mechanics we obtain the statistical averages of the electric polarization and then derive readily an expression for the hyperpolarizability of the paradisubstituted benzenes. Comparisons with experimental observations and other quantum calculations of the hyperpolarizabilities for the paradisubstituted benzenes are made qualitatively and quantitatively. These results imply that the DLA method appears useful in describing the nonlinear optical phenomena in the substituted benzene molecules. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem 93: 335–343, 2003 相似文献
87.
Shuang Zhang 《K-Theory》1992,6(1):1-27
We first determine the homotopy classes of nontrivial projections in a purely infinite simpleC*-algebraA, in the associated multiplier algebraM(A) and the corona algebraM
A/A in terms ofK
*(A). Then we describe the generalized Fredholm indices as the group of homotopy classes of non-trivial projections ofA; consequently, we determine theK
*-groups of all hereditaryC*-subalgebras of certain corona algebras. Secondly, we consider a group structure of *-isomorphism classes of hereditaryC*-subalgebras of purely infinite simpleC*-algebras. In addition, we prove that ifA is aC*-algebra of real rank zero, then each unitary ofA, in caseA it unital, each unitary ofM(A) and ofM(A)/A, in caseA is nonunital but -unital, can be factored into a product of a unitary homotopic to the identity and a unitary matrix whose entries are all partial isometries (with respect to a decomposition of the identity).Partially supported by a grant from the National Science Foundation. 相似文献
88.
A. Daele 《K-Theory》1992,6(5):465-485
LetA be a real or complex Banach algebra and assume that is an action of a finite groupG onA by means of continuous automorphisms. To such a finite covariant system (A, G, ), we associate an Abelian groupK(A, G, ). We obtain some classical exact sequences for an algebraA and a closed invariant idealI. We also compute the group in a few important special cases. Doing so, we relate our new invariant to the classicalK
0 andK
1 of a Banach algebra and to theK-theory of 2-graded Banach algebras. Finally, we obtain a result that gives a close relationship of our groupK(A, G, ) with theK-theory of the crossed productA
G. In particular, we prove a six-term exact sequence involving our groupK(A, G, ) and theK-groups ofA
G. In this way, we hope to contribute to the well-known problem of finding theK-theory of the crossed productA
G in the case of an action of a finite group. 相似文献
89.
Irreducible covariant tensor modules for the Lie supergroups GL(m/n) and the Lie superalgebras gl(m/n) and sl(m/n) are obtained through the use of Young tableaux techniques. The starting point is the graded permutation action, first introduced by Dondi and Jarvis, on V
l
. The isomorphism between this group of actions and the symmetric group S
l enables the graded generalization of the Young symmetrizers, and hence of the column relations and Garnir relations, to be made. Consequently, corresponding to each partition of l an irreducible GL(m/n) module may be obtained as a submodule of V
l
. A basis for the module labeled by the partition is provided by GL(m/n)–standard tableaux of shape defined by Berele and Regev. The reduction of an arbitrary tableau to standard form is accomplished through the use of graded column relations and graded Garnir relations. The standardization procedure is algorithmic and allows matrix representations of the Lie superalgebras gl(m/n) and sl(m/n) to be constructed explicitly over the field of rational numbers. All the various steps of the standardization algorithm are exemplified, as well as the explicit construction of matrices representing particular elements of gl(m/n) and sl(m/n). 相似文献
90.
Craig C. Martens 《Journal of statistical physics》1992,68(1-2):207-237
We describe our work on qualitative methods for visualizing the quantum eigenstates of systems with nonlinear classical dynamics. For two-degree-of-freedom systems, our approach is based on the use of generalized coherent states, and allows systems with nonoscillator kinematics to be investigated. The general approach is illustrated with two examples involving vibration-rotation interaction in polyatomic molecules. We apply the coherent states of the Lie groupH
4SU(2) to define quantum surfaces of section for a model involving centrifugal coupling of a harmonic bend with molecular rotation, andSU(2)SU(2) coherent states to study two harmonic normal modes coupled to overall molecular rotation through coriolis interaction. In both systems, quantum states are visualized on the rotational surface of section and compared with the corresponding classical phase space structure. Striking classical-quantum correspondence is observed. We then describe recent results on the quantum states of (N 3)-dimensional systems of coupled nonlinear oscillators, which reveal a quantum delocalization that is reminiscent of classical Arnold diffusion. 相似文献