E6 unification model building iI. Clebsch-Gordan coefficients of 78⊗78

Journal of Mathematical Physics

Volumn 41, Issue 12, 2000, Pages 8170-8189

  Anderson, Gregory W ^a   Blažek, Tomáš ^a,b  

^a NORTHWESTERN UNIVERSITY   (United States)

^b Faculty of Natural Sciences   (Slovakia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034361304     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1308077     Document Type: Article

References (18)

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2. L-G. Koh, J. Patera, and C. Rousseau, J. Math. Phys. 25, 2863 (1984).
3. 6 unification model building I: Clebsch-Gordan coefficients of 27⊗27," J. Math. Phys. 41, 4808 (2000).
4. B. R. Judd, W. Miller, Jr., J. Patera, and P. Winternitz, J. Math. Phys. 15, 1787 (1974); E. M. Haacke, J. W. Moffat, and P. Savaria, ibid. 17, 2041 (1976); R. C. King, J. Phys. A 14, 77 (1981), and references to the earlier work therein; T. H. Seligman and R. T. Sharp, J. Math. Phys. 24, 769 (1983).
5. B. R. Judd, W. Miller, Jr., J. Patera, and P. Winternitz, J. Math. Phys. 15, 1787 (1974); E. M. Haacke, J. W. Moffat, and P. Savaria, ibid. 17, 2041 (1976); R. C. King, J. Phys. A 14, 77 (1981), and references to the earlier work therein; T. H. Seligman and R. T. Sharp, J. Math. Phys. 24, 769 (1983).
6. B. R. Judd, W. Miller, Jr., J. Patera, and P. Winternitz, J. Math. Phys. 15, 1787 (1974); E. M. Haacke, J. W. Moffat, and P. Savaria, ibid. 17, 2041 (1976); R. C. King, J. Phys. A 14, 77 (1981), and references to the earlier work therein; T. H. Seligman and R. T. Sharp, J. Math. Phys. 24, 769 (1983).
7. B. R. Judd, W. Miller, Jr., J. Patera, and P. Winternitz, J. Math. Phys. 15, 1787 (1974); E. M. Haacke, J. W. Moffat, and P. Savaria, ibid. 17, 2041 (1976); R. C. King, J. Phys. A 14, 77 (1981), and references to the earlier work therein; T. H. Seligman and R. T. Sharp, J. Math. Phys. 24, 769 (1983).
8. S.-P. Li, R. V. Moody, M. Nicolescu, and J. Patera, J. Math. Phys. 27, 668 (1986).
9. The simplest example for such an inequality would be the SU(2) relation 2|m|≤2l, understood in the sense that the SU(2) ladder operator can be applied to the highest weight (2l) up to 2|m| times when constructing a particular representation.
10. M. A. del Olmo, J. Patera, M. A. Rodriquez, and C. Rousseau, J. Math. Phys. 28, 258 (1987).
11. In our conventions, all states are normalized to one.
12. R. Slansky, Phys. Rep. 79, 1 (1981).
13. 6 tensor products of the 27 with higher dimensionaJ representations, (in preparation).
14. R. V. Moody and J. Patera, J. Math. Phys. 25, 2838 (1984).
15. c, and S of the 27 acquire very heavy masses and that is why they have not been observed. In N > 1 supersymmetry, the 78 in this operator contains vector particles that may be identified with the observed gauge bosons.
16. 3, a member of the isospin triplet, is the orthogonal (0 0) weight state. This notation is used in Eq. (22).
17. C. Caso et al., The European Physical Journal C3 (1998) 1. Available also at http://pdg.lbl.gov/1998/ su3rpp.ps.
18. This new phase convention could, e.g., impose a sign change for every 78 superfield component with a bar. Note the singlet in the 78⊗78 then becomes a trace in terms of the physical superfield components.