on E6

  • for E6 down to SU(6)xSU(2)
    • 27 = (6, 2) + (15, 1)
  • SU(6) → SU(4)×SU(2)×U(1)
    • 6 = (1, 2)(−2) + (4, 1)(1)
      15 = (1, 1)(−4) + (4, 2)(−1) + (6, 1)(2)
  • SU(6) → SU(3)×SU(3)×U(1)
    6 = (3, 1)(1) + (1, 3)(−1)
    15 = (3, 1)(2) + (1, 3)(−2) + (3, 3)(0)
  • SU(4) → SU(3)×U(1)
    4 = (1)(−3) + (3)(1)
    6 = (3)(−2) + (3)(2)
  • SU(4) → SU(2)×SU(2)×U(1)
    4 = (2, 1)(1) + (1, 2)(−1)
    6 = (1, 1)(2) + (1, 1)(−2) + (2, 2)(0)
  • SU(3) → SU(2)×U(1)
    3 = (1)(−2) + (2)(1)
  • 6 = (1)(−4) + (2)(−1) + (3)(2)
    8 = (1)(0) + (2)(3) + (2)(−3) + (3)(0)

more tables in https://arxiv.org/abs/1511.08771

  • so7 ⊃ su2 ⊕ su2 ⊕ su2(R)
    • 27 = (3, 3, 1) ⊕ (2, 2, 3) ⊕ (1, 1, 5) ⊕ (1, 1, 1)
  • so7 ⊃ usp4 ⊕ u1(R)
    • 27 = (14)(0) ⊕ (5)(2) ⊕ (5)(−2) ⊕ (1)(4) ⊕ (1)(0) ⊕ (1)(−4)
  • so27 ⊃ so24 ⊕ su2(R)
    • 27 = (24, 1) ⊕ (1, 3)
  • so27 ⊃ so12 ⊕ so15(R)
    • 27 = (12, 1) ⊕ (1, 15)
  • usp8 ⊃ su4 ⊕ u1(R)
    • 27 = (15)(0) ⊕ (6)(2) ⊕ (6)(−2)
  • usp8 ⊃ su2 ⊕ usp6
    • 27 = (2, 6) ⊕ (1, 14) ⊕ (1, 1)

quizas tambien desde 26 si hay un singlete que va aparte, o desde 28 si estamos dispuestos a aceptar un lepton extra

  • F4 ⊃ su2 ⊕ usp6(R)
    • 26 = (2, 6) ⊕ (1, 14)

usp6

usp6 ⊃ su3 ⊕ u1(R) 1 = (1)(0) 6 = (3)(1) ⊕ (3)(−1) 14 = (8)(0) ⊕ (3)(−2) ⊕ (3)(2) 14′ = (6)(−1) ⊕ (6)(1) ⊕ (1)(3) ⊕ (1)(−3)

usp6 ⊃ su2 ⊕ usp4 (R) 1 = (1, 1) 6 = (2, 1) ⊕ (1, 4) 14 = (2, 4) ⊕ (1, 5) ⊕ (1, 1) 14′ = (2, 5) ⊕ (1, 4)

usp6 ⊃ su2 ⊕ su2(S) 1 = (1, 1) 6 = (3, 2) 14 = (5, 1) ⊕ (3, 3) 14′ = (5, 2) ⊕ (1, 4)

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