The decomposition of the tensor product of a positive and a negative discrete series representation of the Lie algebra su(1, 1) is a direct integral over the principal unitary series representations. In the decomposition discrete terms can occur, and the discrete terms are a finite number of discrete series representations or one complementary series representation. The interpretation of Meixne...

This paper characterizes the first cohomology group H(G,M) where M is a Banach space (with norm || ||M) that is also a left CG module such that the elements of G act onM as continuous C-linear transformations. We study this group for G an infinite, finitely generated group. Of particular interest are the implications of the vanishing of the group H(G,M). The first result is that H(G,CG) imbeds ...

The non-relativistic quark model has been a useful tool in the study of hadrons. Baryons and mesons are described by quantum mechanical wavefunctions for nonrelativistic constituent quarks. The lowest lying baryons, the 81/2 and 103/2, are three quark states with wavefunctions which are completely antisymmetric in color, and completely symmetric in position and spin-flavor. The properties of ba...

We present a program that allows for the computation of tensor products of irreducible representations of Lie algebras A−G based on the explicit construction of weight states. This straightforward approach (which is slower and more memoryconsumptive than the standard methods to just calculate dimensions of the tensor product decomposition) produces Clebsch-Gordan coefficients that are of intere...

After careful introduction and discussion of the concepts involved, procedures are developed to compute Racah and Clebsch-Gordan coefficients for general r-fold tensor products of the U(N) groups. In the process, the multiplicity of a given irreducible representation (irrep) in the direct sum basis is computed, and generalized Casimir operators are introduced to uniquely label the multiple irre...

We study the tensor category of modules over a semisimple bialgebra H under the assumption that irreducible H -modules of the same dimension >1 are isomorphic. We consider properties of Clebsch–Gordan coefficients showing multiplicities of occurrences of each irreducible H -module in a tensor product of irreducible ones. It is shown that, in general, these coefficients cannot have small values....

In this article, the author argues on importance of Reformation. Despite over 500 years has passed since reformation, roman catholic church not moved towards true understanding gospel, in terms justification as being declared right. Furthermore, author's context American Evangelism, pelagianism seems taking mindset biblically illiterate. The preaching evangel that justifies ungodly must be call...

The Muslim world is in crisis – politically, socially and economically Islam need of a reformation. Drawing on insights from the Protestant Reformation, this article argues that two major reasons for success Reformation lay fact dissident voices such as Martin Luther were protected developments like printing press increased literacy thereby empowering ordinary people to read Bible their own wit...

The presence of auxin (2,4-D), in the culture medium of tobacco (Nicotiana tabacum var Maryland) mesophyll protoplasts is necessary both for cell wall regeneration and for passage of the cells from phase G(0) to phase G(1) of the cell cycle. Among about 250 proteins synthesized by protoplasts and characterized by their migration in a two-dimensional electrophoresis gel, 2,4-dichlorophenoxyaceti...