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)