Highest vectors of representations (total 10) ; the vectors are over the primal subalgebra. | g3+g−7 | h4 | g7+g−3 | g13+g2+5/3g1 | g14 | g19 | g22+1/2g17 | g21 | g20 | g24 |
weight | 0 | 0 | 0 | 2ω1 | 6ω1 | 6ω1 | 6ω1 | 6ω1 | 6ω1 | 10ω1 |
weights rel. to Cartan of (centralizer+semisimple s.a.). | −ψ | 0 | ψ | 2ω1 | 6ω1−2ψ | 6ω1−ψ | 6ω1 | 6ω1+ψ | 6ω1+2ψ | 10ω1 |
Isotypical components + highest weight | V−ψ → (0, -1) | V0 → (0, 0) | Vψ → (0, 1) | V2ω1 → (2, 0) | V6ω1−2ψ → (6, -2) | V6ω1−ψ → (6, -1) | V6ω1 → (6, 0) | V6ω1+ψ → (6, 1) | V6ω1+2ψ → (6, 2) | V10ω1 → (10, 0) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Module label | W1 | W2 | W3 | W4 | W5 | W6 | W7 | W8 | W9 | W10 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Module elements (weight vectors). In blue - corresp. F element. In red -corresp. H element. |
| Cartan of centralizer component.
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| 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 | 0 | 0 | 2ω1 0 −2ω1 | 6ω1 4ω1 2ω1 0 −2ω1 −4ω1 −6ω1 | 6ω1 4ω1 2ω1 0 −2ω1 −4ω1 −6ω1 | 6ω1 4ω1 2ω1 0 −2ω1 −4ω1 −6ω1 | 6ω1 4ω1 2ω1 0 −2ω1 −4ω1 −6ω1 | 6ω1 4ω1 2ω1 0 −2ω1 −4ω1 −6ω1 | 10ω1 8ω1 6ω1 4ω1 2ω1 0 −2ω1 −4ω1 −6ω1 −8ω1 −10ω1 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Weights of elements in (fundamental coords w.r.t. Cartan of subalgebra) + Cartan centralizer | −ψ | 0 | ψ | 2ω1 0 −2ω1 | 6ω1−2ψ 4ω1−2ψ 2ω1−2ψ −2ψ −2ω1−2ψ −4ω1−2ψ −6ω1−2ψ | 6ω1−ψ 4ω1−ψ 2ω1−ψ −ψ −2ω1−ψ −4ω1−ψ −6ω1−ψ | 6ω1 4ω1 2ω1 0 −2ω1 −4ω1 −6ω1 | 6ω1+ψ 4ω1+ψ 2ω1+ψ ψ −2ω1+ψ −4ω1+ψ −6ω1+ψ | 6ω1+2ψ 4ω1+2ψ 2ω1+2ψ 2ψ −2ω1+2ψ −4ω1+2ψ −6ω1+2ψ | 10ω1 8ω1 6ω1 4ω1 2ω1 0 −2ω1 −4ω1 −6ω1 −8ω1 −10ω1 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Single module character over Cartan of s.a.+ Cartan of centralizer of s.a. | M−ψ | M0 | Mψ | M2ω1⊕M0⊕M−2ω1 | M6ω1−2ψ⊕M4ω1−2ψ⊕M2ω1−2ψ⊕M−2ψ⊕M−2ω1−2ψ⊕M−4ω1−2ψ⊕M−6ω1−2ψ | M6ω1−ψ⊕M4ω1−ψ⊕M2ω1−ψ⊕M−ψ⊕M−2ω1−ψ⊕M−4ω1−ψ⊕M−6ω1−ψ | M6ω1⊕M4ω1⊕M2ω1⊕M0⊕M−2ω1⊕M−4ω1⊕M−6ω1 | M6ω1+ψ⊕M4ω1+ψ⊕M2ω1+ψ⊕Mψ⊕M−2ω1+ψ⊕M−4ω1+ψ⊕M−6ω1+ψ | M6ω1+2ψ⊕M4ω1+2ψ⊕M2ω1+2ψ⊕M2ψ⊕M−2ω1+2ψ⊕M−4ω1+2ψ⊕M−6ω1+2ψ | M10ω1⊕M8ω1⊕M6ω1⊕M4ω1⊕M2ω1⊕M0⊕M−2ω1⊕M−4ω1⊕M−6ω1⊕M−8ω1⊕M−10ω1 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Isotypic character | M−ψ | M0 | Mψ | M2ω1⊕M0⊕M−2ω1 | M6ω1−2ψ⊕M4ω1−2ψ⊕M2ω1−2ψ⊕M−2ψ⊕M−2ω1−2ψ⊕M−4ω1−2ψ⊕M−6ω1−2ψ | M6ω1−ψ⊕M4ω1−ψ⊕M2ω1−ψ⊕M−ψ⊕M−2ω1−ψ⊕M−4ω1−ψ⊕M−6ω1−ψ | M6ω1⊕M4ω1⊕M2ω1⊕M0⊕M−2ω1⊕M−4ω1⊕M−6ω1 | M6ω1+ψ⊕M4ω1+ψ⊕M2ω1+ψ⊕Mψ⊕M−2ω1+ψ⊕M−4ω1+ψ⊕M−6ω1+ψ | M6ω1+2ψ⊕M4ω1+2ψ⊕M2ω1+2ψ⊕M2ψ⊕M−2ω1+2ψ⊕M−4ω1+2ψ⊕M−6ω1+2ψ | M10ω1⊕M8ω1⊕M6ω1⊕M4ω1⊕M2ω1⊕M0⊕M−2ω1⊕M−4ω1⊕M−6ω1⊕M−8ω1⊕M−10ω1 |
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