Highest vectors of representations (total 10) ; the vectors are over the primal subalgebra. | g−2 | h2 | g2 | g9+5/9g8+8/9g4 | −g11+8/5g7 | −g14+8/5g10 | −g19+8/5g16 | g22 | g23 | g24 |
weight | 0 | 0 | 0 | 2ω1 | 3ω1 | 3ω1 | 6ω1 | 9ω1 | 9ω1 | 10ω1 |
weights rel. to Cartan of (centralizer+semisimple s.a.). | −4ψ | 0 | 4ψ | 2ω1 | 3ω1−2ψ | 3ω1+2ψ | 6ω1 | 9ω1−2ψ | 9ω1+2ψ | 10ω1 |
Isotypical components + highest weight | V−4ψ → (0, -4) | V0 → (0, 0) | V4ψ → (0, 4) | V2ω1 → (2, 0) | V3ω1−2ψ → (3, -2) | V3ω1+2ψ → (3, 2) | V6ω1 → (6, 0) | V9ω1−2ψ → (9, -2) | V9ω1+2ψ → (9, 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 | 3ω1 ω1 −ω1 −3ω1 | 3ω1 ω1 −ω1 −3ω1 | 6ω1 4ω1 2ω1 0 −2ω1 −4ω1 −6ω1 | 9ω1 7ω1 5ω1 3ω1 ω1 −ω1 −3ω1 −5ω1 −7ω1 −9ω1 | 9ω1 7ω1 5ω1 3ω1 ω1 −ω1 −3ω1 −5ω1 −7ω1 −9ω1 | 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 | −4ψ | 0 | 4ψ | 2ω1 0 −2ω1 | 3ω1−2ψ ω1−2ψ −ω1−2ψ −3ω1−2ψ | 3ω1+2ψ ω1+2ψ −ω1+2ψ −3ω1+2ψ | 6ω1 4ω1 2ω1 0 −2ω1 −4ω1 −6ω1 | 9ω1−2ψ 7ω1−2ψ 5ω1−2ψ 3ω1−2ψ ω1−2ψ −ω1−2ψ −3ω1−2ψ −5ω1−2ψ −7ω1−2ψ −9ω1−2ψ | 9ω1+2ψ 7ω1+2ψ 5ω1+2ψ 3ω1+2ψ ω1+2ψ −ω1+2ψ −3ω1+2ψ −5ω1+2ψ −7ω1+2ψ −9ω1+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−4ψ | M0 | M4ψ | M2ω1⊕M0⊕M−2ω1 | M3ω1−2ψ⊕Mω1−2ψ⊕M−ω1−2ψ⊕M−3ω1−2ψ | M3ω1+2ψ⊕Mω1+2ψ⊕M−ω1+2ψ⊕M−3ω1+2ψ | M6ω1⊕M4ω1⊕M2ω1⊕M0⊕M−2ω1⊕M−4ω1⊕M−6ω1 | M9ω1−2ψ⊕M7ω1−2ψ⊕M5ω1−2ψ⊕M3ω1−2ψ⊕Mω1−2ψ⊕M−ω1−2ψ⊕M−3ω1−2ψ⊕M−5ω1−2ψ⊕M−7ω1−2ψ⊕M−9ω1−2ψ | M9ω1+2ψ⊕M7ω1+2ψ⊕M5ω1+2ψ⊕M3ω1+2ψ⊕Mω1+2ψ⊕M−ω1+2ψ⊕M−3ω1+2ψ⊕M−5ω1+2ψ⊕M−7ω1+2ψ⊕M−9ω1+2ψ | M10ω1⊕M8ω1⊕M6ω1⊕M4ω1⊕M2ω1⊕M0⊕M−2ω1⊕M−4ω1⊕M−6ω1⊕M−8ω1⊕M−10ω1 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Isotypic character | M−4ψ | M0 | M4ψ | M2ω1⊕M0⊕M−2ω1 | M3ω1−2ψ⊕Mω1−2ψ⊕M−ω1−2ψ⊕M−3ω1−2ψ | M3ω1+2ψ⊕Mω1+2ψ⊕M−ω1+2ψ⊕M−3ω1+2ψ | M6ω1⊕M4ω1⊕M2ω1⊕M0⊕M−2ω1⊕M−4ω1⊕M−6ω1 | M9ω1−2ψ⊕M7ω1−2ψ⊕M5ω1−2ψ⊕M3ω1−2ψ⊕Mω1−2ψ⊕M−ω1−2ψ⊕M−3ω1−2ψ⊕M−5ω1−2ψ⊕M−7ω1−2ψ⊕M−9ω1−2ψ | M9ω1+2ψ⊕M7ω1+2ψ⊕M5ω1+2ψ⊕M3ω1+2ψ⊕Mω1+2ψ⊕M−ω1+2ψ⊕M−3ω1+2ψ⊕M−5ω1+2ψ⊕M−7ω1+2ψ⊕M−9ω1+2ψ | M10ω1⊕M8ω1⊕M6ω1⊕M4ω1⊕M2ω1⊕M0⊕M−2ω1⊕M−4ω1⊕M−6ω1⊕M−8ω1⊕M−10ω1 |