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...

This paper deals with a dynamical system that generalizes the Kepler-Coulomb system and the Hartmann system. It is shown that the Schrödinger equation for this generalized KeplerCoulomb system can be separated in prolate spheroidal coordinates. The coefficients of the interbasis expansions between three bases (spherical, parabolic and spheroidal) are studied in detail. It is found that the coef...

Representation theory for the Jordanian quantum algebra Uh(sl(2)) is developed using a nonlinear relation between its generators and those of sl(2). Closed form expressions are given for the action of the generators of Uh(sl(2)) on the basis vectors of finite dimensional irreducible representations. In the tensor product of two such representations, a new basis is constructed on which the gener...

We propose a new realization of the elliptic quantum group equipped with the H-Hopf algebroid structure on the basis of the elliptic algebra Uq,p(ŝl2). The algebra Uq,p(ŝl2) has a constructive definition in terms of the Drinfeld generators of the quantum affine algebra Uq(ŝl2) and a Heisenberg algebra. This yields a systematic construction of both finite and infinite-dimensional dynamical repre...

In this article the full set of irreducible unitary holomorphic representations of U (p, q) is determined. For a general Hermitian symmetric space G/K of the noncompact type the set of irreducible unitary representations of G on scalar valued holomorphic functions has been found by Wallach [14] and by Rossi and Vergne [11]. For the groups Mp(n, ~) and SU(n, n) unitary irreducible representation...

The structure constants of quantum Lie algebras depend on a quantum deformation parameter q and they reduce to the classical structure constants of a Lie algebra at q = 1. We explain the relationship between the structure constants of quantum Lie algebras and quantum Clebsch-Gordan coefficients for adjoint ⊗ adjoint → adjoint. We present a practical method for the determination of these quantum...

The theory of apolarity was first developed by Clebsch, Lasker, Richw x mond, Sylvester, and Wakeford 10, 17, 20 . They were first interested in studying homogeneous polynomials of degree p and in q variables, and in expressing them as sums of pth powers of linear terms. The problem is to minimize the number of pth powers which are required in such a sum. For instance, a result due to Sylvester...