By Helmer Aslaksen, Eng-Chye Tan, Chen-bo Zhu (auth.), Bruno Gruber (eds.)
Invariant conception of Matrices; H. Aslaksen, et al. Symmetries of easy debris Revisited; A.O. Barut. Perturbative SU(1,1); H.Beker. A twin constitution for the Quantal Rotation staff, SU(2); L.C.Biedenharn, M.A. Lohe. a few issues within the Quantization of Relativistic Grassmann based interplay structures; A. Del Sol Mesa, R.P.Martinez y Romero. q-Difference Intertwining Operators for Uq(sI(4)) and q-Conformal Invariant Equations; V.K. Dobrev. A Quantum Mechanical Evolution Equation for combined States from Symmetry and Kinematics; H.D.Doebner, J.D. Hennig. Quantum Mechanical Motions over the gang Manifolds and similar Potentials; I.H. Duru. Quantum Violation of vulnerable Equivalence crucial within the Brans-Dicke thought; Y. Fujii. Quantum Unitary and Pseudounitary teams and Generalized Hadron Mass family; A.M. Gavrilik. Linear Coxeter teams; J. Getino. Diffeomorphism teams, Quasiinvariant Measures, and endless Quantum platforms; G.A. Goldin, U. Moschella. Algebraic Shells and the Interacting Boson version of the Nucleus; B. Gruber. fresh advancements within the software of Vector Coherent States; K.T. Hecht. Algebraic conception of the Threebody challenge; F. Iachello. 18 extra articles. Index.
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It is very useful for the further development of this idea to have an explicit realization of the corresponding (6 - j) operators as linear operators on a well-defined set of vector spaces which carry irreps of the dual algebra. That such a realization exists  is in itself rather surprising. Consider the unitary group U(3). Then the complete set of (integral) unitary irreps can be labelled by the Young frames denoted by [m] == [m13m23m33], where the mi3 are (positive, negative or zero) integers such that m13 ~ m23 ~ m33.
We will denote the coupling effected by the (6-j) operators by the symbol D. 3). 9), identify the coupling 0 by (6-j) coefficients to be the analog-for the dual Hopf algebra-of the coupling x by the wee coefficients for the SU(2) Hopf algebra. It follows that we can determine both the algebra and the co-algebra structure of the dual Hopf algebra from the (6- j) coupling coefficients. 3 The Dual Algebra We have stated (in Section 2) that the coupling law for the group (the WCG coefficients) determines the Lie algebra structure.
2 These operators are of two types - differential and integral. For the canonical construction of the integral invariant operators (which we shall not consider) we refer to . As stated we are interested in the invariant differential operators. , , however, most of these rely on constructions which are not yet available for quantum groups. Here we shall apply a procedure  which is rather algebraic and can be generalized almost straightforwardly to quantum groups. 3. 2. Here we shall sketch the procedure of  illustrating the general notions with the conformal group SU(2,2).
Symmetries in Science VIII by Helmer Aslaksen, Eng-Chye Tan, Chen-bo Zhu (auth.), Bruno Gruber (eds.)