In [AO] the authors study Steiner bundles via their unstable hyperplanes and proved that (see [AO], Tmm 5.9) : A rank n Steiner bundle on Pn which is SL(2,C) invariant is a Schwarzenberger bundle. In this note we give a very short proof of this result based on Clebsch-Gordon problem for SL(2,C)modules.

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 a simple method to calculate corresponding coefficients in terms of the Askey-Wilson polynomials is proposed.

The complex analytic methods have found a wide range of applications in the study of multiplicity-free representations. This article discusses, in particular, its applications to the question of restricting highest weight modules with respect to reductive symmetric pairs. We present a number of multiplicity-free branching theorems that include the multiplicity-free property of some of known res...

The Clebsch-Gordan and Racah-Wigner coefficients for the positive (or negative) discrete series of irreducible representations for the noncompact form Uq(SU(1, 1)) of the algebra Uq(sl(2)) are computed. n0. Introduction Now it is well known the great significance which the Clebsch-Gordan and RacahWigner coefficients for the algebra Uq(SU(2)) has in the conformal field theory, topological field ...

In the theory of Clebsch-Gordan coefficients, one may recognize domain space as set weakly semi-magic squares size three. Two partitions on this are considered: a triangle-hexagon model based top lines, and orbits under finite group action. addition to giving another proof McMahon's formula, we give generating function that counts so-called trivial zeros coefficients its associated quasi-polyno...

We obtain the affine Euler-Poincaré equations by standard Lagrangian reduction and deduce the associated Clebsch-constrained variational principle. These results are illustrated in deriving the equations of motion for continuum spin systems and Kirchhoff’s rod, where they provide a unified geometric interpretation.

The irreducible representations of the cubic space group are described and used to determine the mapping of continuum states to lattice states with non-zero linear momentum. The Clebsch-Gordan decomposition is calculated from the character table for the cubic space group. These results are used to identify multiparticle states which appear in the hadron spectrum on the lattice.

The structure of r-fold tensor products of irreducible tame representations of U(∞) = lim −→U(n) are described, versions of contragredient representations and invariants are realized, and methods of calculating multiplicities, Clebsch-Gordan and Racah coefficients are given using invariant theory on Bargmann-Segal-Fock spaces. PACS codes: 02.20.Tw, 02.20.QS, 03.65.Fd