Highest vectors of representations (total 9) ; the vectors are over the primal subalgebra. | −h6−2h5+2h3+h1 | g34 | g32 | g11 | g6 | g33 | g7 | g1 | g24 |
weight | 0 | ω1+ω3 | ω1+ω4 | ω3+ω4 | 2ω4 | ω1+ω5 | ω3+ω5 | 2ω5 | ω2+ω4+ω5 |
weights rel. to Cartan of (centralizer+semisimple s.a.). | 0 | ω1+ω3 | ω1+ω4+6ψ | ω3+ω4−6ψ | 2ω4 | ω1+ω5−6ψ | ω3+ω5+6ψ | 2ω5 | ω2+ω4+ω5 |
Isotypical components + highest weight | V0 → (0, 0, 0, 0, 0, 0) | Vω1+ω3 → (1, 0, 1, 0, 0, 0) | Vω1+ω4+6ψ → (1, 0, 0, 1, 0, 6) | Vω3+ω4−6ψ → (0, 0, 1, 1, 0, -6) | V2ω4 → (0, 0, 0, 2, 0, 0) | Vω1+ω5−6ψ → (1, 0, 0, 0, 1, -6) | Vω3+ω5+6ψ → (0, 0, 1, 0, 1, 6) | V2ω5 → (0, 0, 0, 0, 2, 0) | Vω2+ω4+ω5 → (0, 1, 0, 1, 1, 0) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Module label | W1 | W2 | W3 | W4 | W5 | W6 | W7 | W8 | W9 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Module elements (weight vectors). In blue - corresp. F element. In red -corresp. H element. | Cartan of centralizer component.
| Semisimple subalgebra component.
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Weights of elements in fundamental coords w.r.t. Cartan of subalgebra in same order as above | 0 | ω1+ω3 −ω1+ω2+ω3 ω1+ω2−ω3 −ω2+2ω3 −ω1+2ω2−ω3 2ω1−ω2 0 0 0 ω1−2ω2+ω3 ω2−2ω3 −2ω1+ω2 −ω1−ω2+ω3 ω1−ω2−ω3 −ω1−ω3 | ω1+ω4 −ω1+ω2+ω4 ω1−ω4 −ω2+ω3+ω4 −ω1+ω2−ω4 −ω3+ω4 −ω2+ω3−ω4 −ω3−ω4 | ω3+ω4 ω2−ω3+ω4 ω3−ω4 ω1−ω2+ω4 ω2−ω3−ω4 −ω1+ω4 ω1−ω2−ω4 −ω1−ω4 | 2ω4 0 −2ω4 | ω1+ω5 −ω1+ω2+ω5 ω1−ω5 −ω2+ω3+ω5 −ω1+ω2−ω5 −ω3+ω5 −ω2+ω3−ω5 −ω3−ω5 | ω3+ω5 ω2−ω3+ω5 ω3−ω5 ω1−ω2+ω5 ω2−ω3−ω5 −ω1+ω5 ω1−ω2−ω5 −ω1−ω5 | 2ω5 0 −2ω5 | ω2+ω4+ω5 ω1−ω2+ω3+ω4+ω5 ω2−ω4+ω5 ω2+ω4−ω5 −ω1+ω3+ω4+ω5 ω1−ω3+ω4+ω5 ω1−ω2+ω3−ω4+ω5 ω1−ω2+ω3+ω4−ω5 ω2−ω4−ω5 −ω1+ω2−ω3+ω4+ω5 −ω1+ω3−ω4+ω5 −ω1+ω3+ω4−ω5 ω1−ω3−ω4+ω5 ω1−ω3+ω4−ω5 ω1−ω2+ω3−ω4−ω5 −ω2+ω4+ω5 −ω1+ω2−ω3−ω4+ω5 −ω1+ω2−ω3+ω4−ω5 −ω1+ω3−ω4−ω5 ω1−ω3−ω4−ω5 −ω2−ω4+ω5 −ω2+ω4−ω5 −ω1+ω2−ω3−ω4−ω5 −ω2−ω4−ω5 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Weights of elements in (fundamental coords w.r.t. Cartan of subalgebra) + Cartan centralizer | 0 | ω1+ω3 −ω1+ω2+ω3 ω1+ω2−ω3 −ω2+2ω3 −ω1+2ω2−ω3 2ω1−ω2 0 0 0 ω1−2ω2+ω3 ω2−2ω3 −2ω1+ω2 −ω1−ω2+ω3 ω1−ω2−ω3 −ω1−ω3 | ω1+ω4+6ψ −ω1+ω2+ω4+6ψ ω1−ω4+6ψ −ω2+ω3+ω4+6ψ −ω1+ω2−ω4+6ψ −ω3+ω4+6ψ −ω2+ω3−ω4+6ψ −ω3−ω4+6ψ | ω3+ω4−6ψ ω2−ω3+ω4−6ψ ω3−ω4−6ψ ω1−ω2+ω4−6ψ ω2−ω3−ω4−6ψ −ω1+ω4−6ψ ω1−ω2−ω4−6ψ −ω1−ω4−6ψ | 2ω4 0 −2ω4 | ω1+ω5−6ψ −ω1+ω2+ω5−6ψ ω1−ω5−6ψ −ω2+ω3+ω5−6ψ −ω1+ω2−ω5−6ψ −ω3+ω5−6ψ −ω2+ω3−ω5−6ψ −ω3−ω5−6ψ | ω3+ω5+6ψ ω2−ω3+ω5+6ψ ω3−ω5+6ψ ω1−ω2+ω5+6ψ ω2−ω3−ω5+6ψ −ω1+ω5+6ψ ω1−ω2−ω5+6ψ −ω1−ω5+6ψ | 2ω5 0 −2ω5 | ω2+ω4+ω5 ω1−ω2+ω3+ω4+ω5 ω2−ω4+ω5 ω2+ω4−ω5 −ω1+ω3+ω4+ω5 ω1−ω3+ω4+ω5 ω1−ω2+ω3−ω4+ω5 ω1−ω2+ω3+ω4−ω5 ω2−ω4−ω5 −ω1+ω2−ω3+ω4+ω5 −ω1+ω3−ω4+ω5 −ω1+ω3+ω4−ω5 ω1−ω3−ω4+ω5 ω1−ω3+ω4−ω5 ω1−ω2+ω3−ω4−ω5 −ω2+ω4+ω5 −ω1+ω2−ω3−ω4+ω5 −ω1+ω2−ω3+ω4−ω5 −ω1+ω3−ω4−ω5 ω1−ω3−ω4−ω5 −ω2−ω4+ω5 −ω2+ω4−ω5 −ω1+ω2−ω3−ω4−ω5 −ω2−ω4−ω5 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Single module character over Cartan of s.a.+ Cartan of centralizer of s.a. | M0 | Mω1+ω3⊕M−ω2+2ω3⊕M−ω1+ω2+ω3⊕M2ω1−ω2⊕Mω1+ω2−ω3⊕Mω1−2ω2+ω3⊕3M0⊕M−ω1+2ω2−ω3⊕M−ω1−ω2+ω3⊕M−2ω1+ω2⊕Mω1−ω2−ω3⊕Mω2−2ω3⊕M−ω1−ω3 | Mω1+ω4+6ψ⊕M−ω2+ω3+ω4+6ψ⊕M−ω1+ω2+ω4+6ψ⊕M−ω3+ω4+6ψ⊕Mω1−ω4+6ψ⊕M−ω2+ω3−ω4+6ψ⊕M−ω1+ω2−ω4+6ψ⊕M−ω3−ω4+6ψ | Mω3+ω4−6ψ⊕Mω1−ω2+ω4−6ψ⊕Mω2−ω3+ω4−6ψ⊕M−ω1+ω4−6ψ⊕Mω3−ω4−6ψ⊕Mω1−ω2−ω4−6ψ⊕Mω2−ω3−ω4−6ψ⊕M−ω1−ω4−6ψ | M2ω4⊕M0⊕M−2ω4 | Mω1+ω5−6ψ⊕M−ω2+ω3+ω5−6ψ⊕M−ω1+ω2+ω5−6ψ⊕M−ω3+ω5−6ψ⊕Mω1−ω5−6ψ⊕M−ω2+ω3−ω5−6ψ⊕M−ω1+ω2−ω5−6ψ⊕M−ω3−ω5−6ψ | Mω3+ω5+6ψ⊕Mω1−ω2+ω5+6ψ⊕Mω2−ω3+ω5+6ψ⊕M−ω1+ω5+6ψ⊕Mω3−ω5+6ψ⊕Mω1−ω2−ω5+6ψ⊕Mω2−ω3−ω5+6ψ⊕M−ω1−ω5+6ψ | M2ω5⊕M0⊕M−2ω5 | Mω1−ω2+ω3+ω4+ω5⊕Mω2+ω4+ω5⊕M−ω1+ω3+ω4+ω5⊕Mω1−ω3+ω4+ω5⊕M−ω2+ω4+ω5⊕M−ω1+ω2−ω3+ω4+ω5⊕Mω1−ω2+ω3−ω4+ω5⊕Mω2−ω4+ω5⊕Mω1−ω2+ω3+ω4−ω5⊕Mω2+ω4−ω5⊕M−ω1+ω3−ω4+ω5⊕Mω1−ω3−ω4+ω5⊕M−ω1+ω3+ω4−ω5⊕Mω1−ω3+ω4−ω5⊕M−ω2−ω4+ω5⊕M−ω1+ω2−ω3−ω4+ω5⊕M−ω2+ω4−ω5⊕M−ω1+ω2−ω3+ω4−ω5⊕Mω1−ω2+ω3−ω4−ω5⊕Mω2−ω4−ω5⊕M−ω1+ω3−ω4−ω5⊕Mω1−ω3−ω4−ω5⊕M−ω2−ω4−ω5⊕M−ω1+ω2−ω3−ω4−ω5 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Isotypic character | M0 | Mω1+ω3⊕M−ω2+2ω3⊕M−ω1+ω2+ω3⊕M2ω1−ω2⊕Mω1+ω2−ω3⊕Mω1−2ω2+ω3⊕3M0⊕M−ω1+2ω2−ω3⊕M−ω1−ω2+ω3⊕M−2ω1+ω2⊕Mω1−ω2−ω3⊕Mω2−2ω3⊕M−ω1−ω3 | Mω1+ω4+6ψ⊕M−ω2+ω3+ω4+6ψ⊕M−ω1+ω2+ω4+6ψ⊕M−ω3+ω4+6ψ⊕Mω1−ω4+6ψ⊕M−ω2+ω3−ω4+6ψ⊕M−ω1+ω2−ω4+6ψ⊕M−ω3−ω4+6ψ | Mω3+ω4−6ψ⊕Mω1−ω2+ω4−6ψ⊕Mω2−ω3+ω4−6ψ⊕M−ω1+ω4−6ψ⊕Mω3−ω4−6ψ⊕Mω1−ω2−ω4−6ψ⊕Mω2−ω3−ω4−6ψ⊕M−ω1−ω4−6ψ | M2ω4⊕M0⊕M−2ω4 | Mω1+ω5−6ψ⊕M−ω2+ω3+ω5−6ψ⊕M−ω1+ω2+ω5−6ψ⊕M−ω3+ω5−6ψ⊕Mω1−ω5−6ψ⊕M−ω2+ω3−ω5−6ψ⊕M−ω1+ω2−ω5−6ψ⊕M−ω3−ω5−6ψ | Mω3+ω5+6ψ⊕Mω1−ω2+ω5+6ψ⊕Mω2−ω3+ω5+6ψ⊕M−ω1+ω5+6ψ⊕Mω3−ω5+6ψ⊕Mω1−ω2−ω5+6ψ⊕Mω2−ω3−ω5+6ψ⊕M−ω1−ω5+6ψ | M2ω5⊕M0⊕M−2ω5 | Mω1−ω2+ω3+ω4+ω5⊕Mω2+ω4+ω5⊕M−ω1+ω3+ω4+ω5⊕Mω1−ω3+ω4+ω5⊕M−ω2+ω4+ω5⊕M−ω1+ω2−ω3+ω4+ω5⊕Mω1−ω2+ω3−ω4+ω5⊕Mω2−ω4+ω5⊕Mω1−ω2+ω3+ω4−ω5⊕Mω2+ω4−ω5⊕M−ω1+ω3−ω4+ω5⊕Mω1−ω3−ω4+ω5⊕M−ω1+ω3+ω4−ω5⊕Mω1−ω3+ω4−ω5⊕M−ω2−ω4+ω5⊕M−ω1+ω2−ω3−ω4+ω5⊕M−ω2+ω4−ω5⊕M−ω1+ω2−ω3+ω4−ω5⊕Mω1−ω2+ω3−ω4−ω5⊕Mω2−ω4−ω5⊕M−ω1+ω3−ω4−ω5⊕Mω1−ω3−ω4−ω5⊕M−ω2−ω4−ω5⊕M−ω1+ω2−ω3−ω4−ω5 |