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51.
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
52.
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
53.
54.
55.
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
56.
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
57.
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
58.
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
59.
The propagation of rough and smooth wall pre-existing turbulent fluid fractures is investigated. The laminar fluid fracture is included as a special case for comparison. Lubrication theory is assumed to apply in the fracture and turbulence is introduced through the wall shear stress. The Perkins–Kern–Nordgren approximation is made in which the fluid pressure is proportional to the half-width of the fracture. The fracture half-width satisfies a non-linear diffusion equation. By using a linear combination of the Lie point symmetries of the non-linear diffusion equation a group invariant solution for the fracture length, volume and half-width is derived. The evolution of the length, half-width and mean flow velocity is analysed for a range of working conditions at the fracture entry. It is found that the mean flow velocity increases approximately linearly along the fracture. 相似文献
60.
Richard Marcuson 《Linear and Multilinear Algebra》2013,61(1):49-55
Recently, Marcuson extended the classical construction of Tits systems in Steinberg groups to include the Kac-Moody Steinberg groups associated with the infinite dimensional versions of the great Lie algebras. If these Lie algebras and their Kac-Moody groups are viewed as limits of their finite dimensional counterparts, more direct methods may be employed. In fact, the Kac-Moody Chevalley groups of these Lie algebras are seen to be simple. 相似文献