A summary of the properties of the Wigner Clebsch-Gordan coefficients and isoscalar factors for the group SU3 in the SU2⊗U1 decomposition is presented. The outer degeneracy problem is discussed in detail with a proof of a conjecture (Braunschweig's) which has been the basis of previous work on the SU3 coupling coefficients. Recursion relations obeyed by the SU3 isoscalar factors are produced, a...

If R, S, T are irreducible SL3(C)-representations, we give an easy and explicit description of a basis of the space of equivariant maps R⊗S → T (Theorem 3.1). We apply this method to the rationality problem for invariant function fields. In particular, we prove the rationality of the moduli space of plane curves of degree 34. This uses a criterion which ensures the stable rationality of some qu...

This article deals with a quantum-mechanical system which generalizes the ordinary isotropic harmonic oscillator system. We give the coefficients connecting the polar and Cartesian bases for D = 2 and the coefficients connecting the Cartesian and cylindrical bases as well as the cylindrical and spherical bases for D = 3. These interbasis expansion coefficients are found to be analytic continuat...

In this article we investigate the structure of a twisted cohomology group of the first homology of a trivalent graph with a coefficient associated with its quantum Clebsch-Gordan condition. By using this investigation we shall show the existence of the external edge cocycles defined in [3] and a finite algorithm to construct such cocycles. Such cocycles are used for a combinatorial realization...

Let G be a group and A a G-algebra. The subrepresentation semiring of A is the set of subrepresentations of A endowed with operations induced by the algebra operations. The introduction of these semirings was motivated by a problem in material science. Typically, physical properties of composite materials are strongly dependent on microstructure. However, in exceptional situations, exact relati...

We propose a non-Abelian generalization of the Clebsch parameterization for a vector in three dimensions. The construction is based on a group-theoretical reduction of the Chern-Simons form on a symmetric space. The formalism is then used to give a canonical (symplectic) discussion of non-Abelian fluid mechanics, analogous to the way the Abelian Clebsch parameterization allows a canonical descr...

GT transitions in N = 28 ∼ 30 nuclei are studied in terms of a large-scale realistic shell-model calculation, by using Towner's microscopic parameters. B(GT) values to low-lying final states are reproduced with a reasonable accuracy. Several gross properties with respect to the GT transitions are investigated with this set of the wavefunctions and the operator. While the calculated total GT − s...

Abstract. We show that multivariable colored link invariants are derived from the roots of unity representations of Uq(g). We propose a property of the Clebsch-Gordan coefficients of Uq(g), which is important for defining the invariants of colored links. For Uq(sl2) we explicitly prove the property, and then construct invariants of colored links and colored ribbon graphs, which generalize the m...

The linearization problem is the problem of finding the coefficients Ck (m,n) in the expansion of the product Pn(x)Qm(x) of two polynomial systems in terms of a third sequence of polynomials Rk (x), Pn(x)Qm(x) = n+m ∑ k=0 Ck (m,n)Rk (x). The polynomials Pn , Qm and Rk may belong to three different polynomial families. In the case P = Q = R, we get the (standard ) linearization or Clebsch-Gordan...