Highest vectors of representations (total 18) ; the vectors are over the primal subalgebra. | g5+g−2 | −h6+1/2h4−1/2h3+h1 | −h5+h2 | g2+g−5 | g11+1/2g3 | g8+2g6 | g10+2g1 | g7+1/2g4 | g14 | g17 | g9 | g15+g12 | g13 | g18 | g20 | g19 | g16 | g21 |
weight | 0 | 0 | 0 | 0 | ω1 | ω1 | ω1 | ω1 | 2ω1 | 2ω1 | 2ω1 | 2ω1 | 2ω1 | 3ω1 | 3ω1 | 3ω1 | 3ω1 | 4ω1 |
weights rel. to Cartan of (centralizer+semisimple s.a.). | −4ψ1+2ψ2 | 0 | 0 | 4ψ1−2ψ2 | ω1−2ψ1−6ψ2 | ω1+2ψ1−8ψ2 | ω1−2ψ1+8ψ2 | ω1+2ψ1+6ψ2 | 2ω1−4ψ1+2ψ2 | 2ω1 | 2ω1 | 2ω1 | 2ω1+4ψ1−2ψ2 | 3ω1−2ψ1−6ψ2 | 3ω1+2ψ1−8ψ2 | 3ω1−2ψ1+8ψ2 | 3ω1+2ψ1+6ψ2 | 4ω1 |
Isotypical components + highest weight | V−4ψ1+2ψ2 → (0, -4, 2) | V0 → (0, 0, 0) | V4ψ1−2ψ2 → (0, 4, -2) | Vω1−2ψ1−6ψ2 → (1, -2, -6) | Vω1+2ψ1−8ψ2 → (1, 2, -8) | Vω1−2ψ1+8ψ2 → (1, -2, 8) | Vω1+2ψ1+6ψ2 → (1, 2, 6) | V2ω1−4ψ1+2ψ2 → (2, -4, 2) | V2ω1 → (2, 0, 0) | V2ω1+4ψ1−2ψ2 → (2, 4, -2) | V3ω1−2ψ1−6ψ2 → (3, -2, -6) | V3ω1+2ψ1−8ψ2 → (3, 2, -8) | V3ω1−2ψ1+8ψ2 → (3, -2, 8) | V3ω1+2ψ1+6ψ2 → (3, 2, 6) | V4ω1 → (4, 0, 0) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Module label | W1 | W2 | W3 | W4 | W5 | W6 | W7 | W8 | W9 | W10 | W11 | W12 | W13 | W14 | W15 | W16 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Module elements (weight vectors). In blue - corresp. F element. In red -corresp. H element. |
| Cartan of centralizer component.
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Weights of elements in fundamental coords w.r.t. Cartan of subalgebra in same order as above | 0 | 0 | 0 | ω1 −ω1 | ω1 −ω1 | ω1 −ω1 | ω1 −ω1 | 2ω1 0 −2ω1 | 2ω1 0 −2ω1 | 2ω1 0 −2ω1 | 2ω1 0 −2ω1 | 3ω1 ω1 −ω1 −3ω1 | 3ω1 ω1 −ω1 −3ω1 | 3ω1 ω1 −ω1 −3ω1 | 3ω1 ω1 −ω1 −3ω1 | 4ω1 2ω1 0 −2ω1 −4ω1 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Weights of elements in (fundamental coords w.r.t. Cartan of subalgebra) + Cartan centralizer | −4ψ1+2ψ2 | 0 | 4ψ1−2ψ2 | ω1−2ψ1−6ψ2 −ω1−2ψ1−6ψ2 | ω1+2ψ1−8ψ2 −ω1+2ψ1−8ψ2 | ω1−2ψ1+8ψ2 −ω1−2ψ1+8ψ2 | ω1+2ψ1+6ψ2 −ω1+2ψ1+6ψ2 | 2ω1−4ψ1+2ψ2 −4ψ1+2ψ2 −2ω1−4ψ1+2ψ2 | 2ω1 0 −2ω1 | 2ω1 0 −2ω1 | 2ω1+4ψ1−2ψ2 4ψ1−2ψ2 −2ω1+4ψ1−2ψ2 | 3ω1−2ψ1−6ψ2 ω1−2ψ1−6ψ2 −ω1−2ψ1−6ψ2 −3ω1−2ψ1−6ψ2 | 3ω1+2ψ1−8ψ2 ω1+2ψ1−8ψ2 −ω1+2ψ1−8ψ2 −3ω1+2ψ1−8ψ2 | 3ω1−2ψ1+8ψ2 ω1−2ψ1+8ψ2 −ω1−2ψ1+8ψ2 −3ω1−2ψ1+8ψ2 | 3ω1+2ψ1+6ψ2 ω1+2ψ1+6ψ2 −ω1+2ψ1+6ψ2 −3ω1+2ψ1+6ψ2 | 4ω1 2ω1 0 −2ω1 −4ω1 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Single module character over Cartan of s.a.+ Cartan of centralizer of s.a. | M−4ψ1+2ψ2 | M0 | M4ψ1−2ψ2 | Mω1−2ψ1−6ψ2⊕M−ω1−2ψ1−6ψ2 | Mω1+2ψ1−8ψ2⊕M−ω1+2ψ1−8ψ2 | Mω1−2ψ1+8ψ2⊕M−ω1−2ψ1+8ψ2 | Mω1+2ψ1+6ψ2⊕M−ω1+2ψ1+6ψ2 | M2ω1−4ψ1+2ψ2⊕M−4ψ1+2ψ2⊕M−2ω1−4ψ1+2ψ2 | M2ω1⊕M0⊕M−2ω1 | M2ω1⊕M0⊕M−2ω1 | M2ω1+4ψ1−2ψ2⊕M4ψ1−2ψ2⊕M−2ω1+4ψ1−2ψ2 | M3ω1−2ψ1−6ψ2⊕Mω1−2ψ1−6ψ2⊕M−ω1−2ψ1−6ψ2⊕M−3ω1−2ψ1−6ψ2 | M3ω1+2ψ1−8ψ2⊕Mω1+2ψ1−8ψ2⊕M−ω1+2ψ1−8ψ2⊕M−3ω1+2ψ1−8ψ2 | M3ω1−2ψ1+8ψ2⊕Mω1−2ψ1+8ψ2⊕M−ω1−2ψ1+8ψ2⊕M−3ω1−2ψ1+8ψ2 | M3ω1+2ψ1+6ψ2⊕Mω1+2ψ1+6ψ2⊕M−ω1+2ψ1+6ψ2⊕M−3ω1+2ψ1+6ψ2 | M4ω1⊕M2ω1⊕M0⊕M−2ω1⊕M−4ω1 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Isotypic character | M−4ψ1+2ψ2 | 2M0 | M4ψ1−2ψ2 | Mω1−2ψ1−6ψ2⊕M−ω1−2ψ1−6ψ2 | Mω1+2ψ1−8ψ2⊕M−ω1+2ψ1−8ψ2 | Mω1−2ψ1+8ψ2⊕M−ω1−2ψ1+8ψ2 | Mω1+2ψ1+6ψ2⊕M−ω1+2ψ1+6ψ2 | M2ω1−4ψ1+2ψ2⊕M−4ψ1+2ψ2⊕M−2ω1−4ψ1+2ψ2 | M2ω1⊕M0⊕M−2ω1 | 2M2ω1⊕2M0⊕2M−2ω1 | M2ω1+4ψ1−2ψ2⊕M4ψ1−2ψ2⊕M−2ω1+4ψ1−2ψ2 | M3ω1−2ψ1−6ψ2⊕Mω1−2ψ1−6ψ2⊕M−ω1−2ψ1−6ψ2⊕M−3ω1−2ψ1−6ψ2 | M3ω1+2ψ1−8ψ2⊕Mω1+2ψ1−8ψ2⊕M−ω1+2ψ1−8ψ2⊕M−3ω1+2ψ1−8ψ2 | M3ω1−2ψ1+8ψ2⊕Mω1−2ψ1+8ψ2⊕M−ω1−2ψ1+8ψ2⊕M−3ω1−2ψ1+8ψ2 | M3ω1+2ψ1+6ψ2⊕Mω1+2ψ1+6ψ2⊕M−ω1+2ψ1+6ψ2⊕M−3ω1+2ψ1+6ψ2 | M4ω1⊕M2ω1⊕M0⊕M−2ω1⊕M−4ω1 |
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