Highest vectors of representations (total 7) ; the vectors are over the primal subalgebra. | −h6−2h5−5/4h4−1/2h3+1/4h2+h1 | g19 | g9+g8 | g4+g2 | g16 | g17 | g13 |
weight | 0 | ω1+ω2 | 2ω3 | 2ω4 | ω1+ω3+ω4 | ω2+ω3+ω4 | 2ω3+2ω4 |
weights rel. to Cartan of (centralizer+semisimple s.a.). | 0 | ω1+ω2 | 2ω3 | 2ω4 | ω1+ω3+ω4+14ψ | ω2+ω3+ω4−14ψ | 2ω3+2ω4 |
Isotypical components + highest weight | V0 → (0, 0, 0, 0, 0) | Vω1+ω2 → (1, 1, 0, 0, 0) | V2ω3 → (0, 0, 2, 0, 0) | V2ω4 → (0, 0, 0, 2, 0) | Vω1+ω3+ω4+14ψ → (1, 0, 1, 1, 14) | Vω2+ω3+ω4−14ψ → (0, 1, 1, 1, -14) | V2ω3+2ω4 → (0, 0, 2, 2, 0) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
Module label | W1 | W2 | W3 | W4 | W5 | W6 | W7 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
Module elements (weight vectors). In blue - corresp. F element. In red -corresp. H element. | Cartan of centralizer component.
| Semisimple subalgebra component.
| Semisimple subalgebra 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+ω2 −ω1+2ω2 2ω1−ω2 0 0 −2ω1+ω2 ω1−2ω2 −ω1−ω2 | 2ω3 0 −2ω3 | 2ω4 0 −2ω4 | ω1+ω3+ω4 −ω1+ω2+ω3+ω4 ω1−ω3+ω4 ω1+ω3−ω4 −ω2+ω3+ω4 −ω1+ω2−ω3+ω4 −ω1+ω2+ω3−ω4 ω1−ω3−ω4 −ω2−ω3+ω4 −ω2+ω3−ω4 −ω1+ω2−ω3−ω4 −ω2−ω3−ω4 | ω2+ω3+ω4 ω1−ω2+ω3+ω4 ω2−ω3+ω4 ω2+ω3−ω4 −ω1+ω3+ω4 ω1−ω2−ω3+ω4 ω1−ω2+ω3−ω4 ω2−ω3−ω4 −ω1−ω3+ω4 −ω1+ω3−ω4 ω1−ω2−ω3−ω4 −ω1−ω3−ω4 | 2ω3+2ω4 2ω4 2ω3 −2ω3+2ω4 0 2ω3−2ω4 −2ω3 −2ω4 −2ω3−2ω4 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
Weights of elements in (fundamental coords w.r.t. Cartan of subalgebra) + Cartan centralizer | 0 | ω1+ω2 −ω1+2ω2 2ω1−ω2 0 0 −2ω1+ω2 ω1−2ω2 −ω1−ω2 | 2ω3 0 −2ω3 | 2ω4 0 −2ω4 | ω1+ω3+ω4+14ψ −ω1+ω2+ω3+ω4+14ψ ω1−ω3+ω4+14ψ ω1+ω3−ω4+14ψ −ω2+ω3+ω4+14ψ −ω1+ω2−ω3+ω4+14ψ −ω1+ω2+ω3−ω4+14ψ ω1−ω3−ω4+14ψ −ω2−ω3+ω4+14ψ −ω2+ω3−ω4+14ψ −ω1+ω2−ω3−ω4+14ψ −ω2−ω3−ω4+14ψ | ω2+ω3+ω4−14ψ ω1−ω2+ω3+ω4−14ψ ω2−ω3+ω4−14ψ ω2+ω3−ω4−14ψ −ω1+ω3+ω4−14ψ ω1−ω2−ω3+ω4−14ψ ω1−ω2+ω3−ω4−14ψ ω2−ω3−ω4−14ψ −ω1−ω3+ω4−14ψ −ω1+ω3−ω4−14ψ ω1−ω2−ω3−ω4−14ψ −ω1−ω3−ω4−14ψ | 2ω3+2ω4 2ω4 2ω3 −2ω3+2ω4 0 2ω3−2ω4 −2ω3 −2ω4 −2ω3−2ω4 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
Single module character over Cartan of s.a.+ Cartan of centralizer of s.a. | M0 | Mω1+ω2⊕M−ω1+2ω2⊕M2ω1−ω2⊕2M0⊕M−2ω1+ω2⊕Mω1−2ω2⊕M−ω1−ω2 | M2ω3⊕M0⊕M−2ω3 | M2ω4⊕M0⊕M−2ω4 | Mω1+ω3+ω4+14ψ⊕M−ω1+ω2+ω3+ω4+14ψ⊕M−ω2+ω3+ω4+14ψ⊕Mω1−ω3+ω4+14ψ⊕Mω1+ω3−ω4+14ψ⊕M−ω1+ω2−ω3+ω4+14ψ⊕M−ω1+ω2+ω3−ω4+14ψ⊕M−ω2−ω3+ω4+14ψ⊕M−ω2+ω3−ω4+14ψ⊕Mω1−ω3−ω4+14ψ⊕M−ω1+ω2−ω3−ω4+14ψ⊕M−ω2−ω3−ω4+14ψ | Mω2+ω3+ω4−14ψ⊕Mω1−ω2+ω3+ω4−14ψ⊕M−ω1+ω3+ω4−14ψ⊕Mω2−ω3+ω4−14ψ⊕Mω2+ω3−ω4−14ψ⊕Mω1−ω2−ω3+ω4−14ψ⊕Mω1−ω2+ω3−ω4−14ψ⊕M−ω1−ω3+ω4−14ψ⊕M−ω1+ω3−ω4−14ψ⊕Mω2−ω3−ω4−14ψ⊕Mω1−ω2−ω3−ω4−14ψ⊕M−ω1−ω3−ω4−14ψ | M2ω3+2ω4⊕M2ω4⊕M2ω3⊕M−2ω3+2ω4⊕M0⊕M2ω3−2ω4⊕M−2ω3⊕M−2ω4⊕M−2ω3−2ω4 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
Isotypic character | M0 | Mω1+ω2⊕M−ω1+2ω2⊕M2ω1−ω2⊕2M0⊕M−2ω1+ω2⊕Mω1−2ω2⊕M−ω1−ω2 | M2ω3⊕M0⊕M−2ω3 | M2ω4⊕M0⊕M−2ω4 | Mω1+ω3+ω4+14ψ⊕M−ω1+ω2+ω3+ω4+14ψ⊕M−ω2+ω3+ω4+14ψ⊕Mω1−ω3+ω4+14ψ⊕Mω1+ω3−ω4+14ψ⊕M−ω1+ω2−ω3+ω4+14ψ⊕M−ω1+ω2+ω3−ω4+14ψ⊕M−ω2−ω3+ω4+14ψ⊕M−ω2+ω3−ω4+14ψ⊕Mω1−ω3−ω4+14ψ⊕M−ω1+ω2−ω3−ω4+14ψ⊕M−ω2−ω3−ω4+14ψ | Mω2+ω3+ω4−14ψ⊕Mω1−ω2+ω3+ω4−14ψ⊕M−ω1+ω3+ω4−14ψ⊕Mω2−ω3+ω4−14ψ⊕Mω2+ω3−ω4−14ψ⊕Mω1−ω2−ω3+ω4−14ψ⊕Mω1−ω2+ω3−ω4−14ψ⊕M−ω1−ω3+ω4−14ψ⊕M−ω1+ω3−ω4−14ψ⊕Mω2−ω3−ω4−14ψ⊕Mω1−ω2−ω3−ω4−14ψ⊕M−ω1−ω3−ω4−14ψ | M2ω3+2ω4⊕M2ω4⊕M2ω3⊕M−2ω3+2ω4⊕M0⊕M2ω3−2ω4⊕M−2ω3⊕M−2ω4⊕M−2ω3−2ω4 |
2 & | -1 & | 0 & | 0\\ |
-1 & | 2 & | 0 & | 0\\ |
0 & | 0 & | 2 & | 0\\ |
0 & | 0 & | 0 & | 2\\ |