The approach of metric–affine field theory is to define spacetime as a real oriented 4-manifold equipped with a metric and an affine connection. The 10 independent components of the metric tensor and the 64 connection coefficients are the unknowns of the theory. We write the Yang–Mills action for the affine connection and vary it both with respect to the metric and the connection. We find a fam...

We evaluate combinatorially certain connection coefficients of the symmetric group that count the number of factorizations of a long cycle as a product of three permutations. Such factorizations admit an important topological interpretation in terms of unicellular constellations on orientable surfaces. Algebraic computation of these coefficients was first done by Jackson using irreducible chara...

We construct rogue waves (RWs) in a coupled two-mode system with the self-focusing nonlinearity of the Manakov type (equal SPM and XPM coefficients), spatially modulated coefficients, and a specially designed external potential. The system may be realized in nonlinear optics and Bose-Einstein condensates. By means of a similarity transformation, we establish a connection between solutions of th...

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....

The generalized hypergeometric function has three singular points 0, 1, and ∞. Connection problem between fundamental solutions at 0 ∞ was completely solved. However, connection 1 been not solved because of holomorphic 1. In this paper, we solve for the function, using analytic continuation integral representation. Namely, all coefficients are products sine cosecant. other words, give a good sy...