I. Quantum Fields as Carriers of the Structure of Space-Time in the Special Grand Unification Model (*G. Stavraki*) |

| 1. Introduction |

| 2. Model |

| | A. Motivation and the general description of the basic equations of the model |

| | B. Heuristic derivation of equation (2) in the framework of the correspondence principle |

| | C. Reduction of the measurement of space-like distances to the measurement of causal intervals in the World with a special (cone) structure |

| | D. The structure of field supermatrix *U* and of equation (2) of the causal proximity algebra |

| 3. Corollaries |

| Acknowledgements |

| References |

II. Group Decomposition in the Special Grand Unification Model in High Energy Physics (*S. Ganebnykh*, *G. Stavraki*) |

| 1. Introduction |

| | A. Symmetry in grand unified models in particle physics |

| | B. Brief description of the special grand unification model (à detailed account see I). Necessity of work with high-dimensional representations of the symmetry group *E*_{6} |

| 2. Algorithm of decomposition of tensor products of *E*_{6} representations |

| | A. The set of *E*_{6} roots and the corresponding split Lie algebra, the set of Weyl group generators, the representation weight multiplicities, and dimension formula |

| | B. Algorithm of finding the basis representations of a decomposition of the tensor product of *E*_{6} algebra representations. Beginning of the computations of the corresponding multiplicities: stage 1 -- the Weyl group construction |

| | C. Stage 2 of multiplicity calculation by formula (16): construction of arrays of vector values of the argument of the partition function *P* |

| | D. Stage 3: Evaluation of the partition function *P* in formula (16) |

| | E. Final stage: direct multiplicity computation by the Kostant formula (16) |

| | F. Results |

| | G. Notes |

| 3. Algorithm of decomposition of *E*_{6} representations into *D*_{5} subalgebra representations |

| | A. Singling out *D*_{5} subalgebra in the algebra *E*_{6}:
splitting the root set and the basis set of algebra generators, and singling out a special generator corresponding to the *U*(1) group degree of freedom |

| | B. Weyl group and dimensional formula for *D*_{5} algebra |

| | C. Comparative description of the algorithms (based on formula (12)) for computation of representation weight multiplicities in *E*_{6}, *D*_{5}, and *A*_{4} algebras |

| | D. Formulas of going over from *E*_{6} to *D*_{5} weights in the description of multiplets |

| | E. Description of *E*_{6} multiplet decomposition into *D*_{5} representations |

| | F. Results |

| | G. Possible physical applications: the first hypothetic superselection rule |

| 4. Algorithm of decomposition of *D*_{5} representations into *A*_{4} representations |

| | A. Selection of the *A*_{4} subalgebra in the subalgebra *D*_{5} Ì *E*_{6} |

| | B. Weyl group and dimensional formula for the *A*_{4} algebra |

| | C. Formulas of transition from *D*_{5}- to *A*_{4}-weights
in the description of multiplets |

| | D. *D*_{5} multiplet decomposition into *A*_{4} representations |

| | E. Results |

| | F. Possible physical applications: the second hypothetical superselection rule |

| 5. Conclusion. Specific prediction of the model |

| Acknowledgements |

| Appendix A |

| Appendix B |

| References |