Related papers: Clebsch-Gordan coefficients, hypergeometric functi…
The angular bispectrum of spherical random fields has recently gained an enormous importance, especially in connection with statistical inference on cosmological data. In this paper, we provide expressions for its moments of arbitrary order…
We obtain exact, simple and very compact expressions for the linearization coefficients of the products of orthogonal polynomials; both the conventional Clebsch-Gordan-type and the modified version. The expressions are general depending…
In this paper we show that a closed form formula for the generalized Clebsch-Gordan integral and the Fourier-Legendre expansion theory allow to evaluate hypergeometric series involving powers of the normalized central binomial coefficient…
We provide an algorithm of computing Clebsch-Gordan coefficients for irreducible representations, with integer weights, of the rotation group SO(3) and demonstrate the convenience of this algorithm for constructing new (to our knowledge)…
An explicit bilinear generating function for Meixner-Pollaczek polynomials is proved. This formula involves continuous dual Hahn polynomials, Meixner-Pollaczek functions, and non-polynomial $_3F_2$-hypergeometric functions that we consider…
Analytic expressions for the Clebsch-Gordan (CG) coefficients of the SO(5) group that involve the 14-dimensional representation can be found in an old paper of M. K. F. Wong. A careful analysis yields that roughly 30% of the coefficients…
The decomposition of tensor products of representations into irreducibles is studied for a continuous family of integrable operator representations of $U_q(sl(2,R)$. It is described by an explicit integral transformation involving a…
Representations of the quantum superalgebra U_q[osp(1/2)] and their relations to the basic hypergeometric functions are investigated. We first establish Clebsch-Gordan decomposition for the superalgebra U_q[osp(1/2)] in which the…
Let $D\geq 1$ and $q\geq 3$ be two integers. Let $H(D)=H(D,q)$ denote the $D$-dimensional Hamming graph over a $q$-element set. Let ${\mathcal T}(D)$ denote the Terwilliger algebra of $H(D)$. Let $V(D)$ denote the standard ${\mathcal…
It has recently been shown that quantum computers can efficiently solve the Heisenberg hidden subgroup problem, a problem whose classical query complexity is exponential. This quantum algorithm was discovered within the framework of using…
It is shown that, in the relativistic hydrogenic approximation, expectation values of the type $\langle n\ell j|r^k|n\ell j\rangle$ can be expressed in terms of Clebsch-Gordan coefficients or $3jm$ symbols. This generalizes the results…
Fast, accurate, and stable computation of the Clebsch-Gordan (C-G) coefficients is always desirable, for example, in light scattering simulations, the translation of the multipole fields, quantum physics and chemistry. Current recursive…
In the theory of Clebsch-Gordan coefficients, one may recognize the domain space as the set of weakly semi-magic squares of size three. Two partitions on this set are considered: a triangle-hexagon model based on top lines, and one based on…
Clebsch-Gordan coefficients of SU(2) and SU(1,1) are defined as eigenfunctions of a linear operator acting on the tensor product of the Hilbert spaces for two irreps of these groups. The shifted harmonic approximation is then used to solve…
The Clebsch--Gordan coefficients of the Kronecker products of the irreducible representations of the Quaternion Group Q8, of the Generalized Quaternion Groups Q16 and Q32, and of the factor group (Q32 X Q32)/{(1,1),(-1,-1)} are computed as…
We compare two approaches to the calculation of irreducible characters of the Lie algebra gl(infinity)^ with negative integral central charge. As a consequence, we obtain a "reciprocity formula" for Clebsch-Gordan coefficients, in the limit…
We show that the Clebsch - Gordan coefficients for the $SU(2)_{p,q}$ - algebra depend on a single parameter Q = $\sqrt{pq}$ ,contrary to the explicit calculation of Smirnov and Wehrhahn [J.Phys.A 25 (1992),5563].
The Askey-Wilson algebra $AW(3)$ with three generators is shown to serve as a hidden symmetry algebra underlying the Racah and (new) generalized Clebsch-Gordan problems for the quantum algebra $sl_q(2)$. On the base of this hidden symmetry…
Bi-partite ribbon graphs arise in organising the large $N$ expansion of correlators in random matrix models and in the enumeration of observables in random tensor models. There is an algebra $\mathcal{K}(n)$, with basis given by bi-partite…
We present a new sum rule for Clebsch-Gordan coefficients using generalized characters of irreducible representations of the rotation group. The identity is obtained from an integral involving Gegenbauer ultraspherical polynomials. A…