Highest vectors of representations (total 11) ; the vectors are over the primal subalgebra. | g−3 | −h5−2h4+2h2+h1 | h3 | g3 | g11+3/4g5+3/4g1 | g9 | g12 | g6 | g10 | g14+g13 | g15 |
weight | 0 | 0 | 0 | 0 | 2ω1 | 3ω1 | 3ω1 | 3ω1 | 3ω1 | 4ω1 | 6ω1 |
weights rel. to Cartan of (centralizer+semisimple s.a.). | −4ψ1 | 0 | 0 | 4ψ1 | 2ω1 | 3ω1−2ψ1−6ψ2 | 3ω1+2ψ1−6ψ2 | 3ω1−2ψ1+6ψ2 | 3ω1+2ψ1+6ψ2 | 4ω1 | 6ω1 |
Isotypical components + highest weight | V−4ψ1 → (0, -4, 0) | V0 → (0, 0, 0) | V4ψ1 → (0, 4, 0) | V2ω1 → (2, 0, 0) | V3ω1−2ψ1−6ψ2 → (3, -2, -6) | V3ω1+2ψ1−6ψ2 → (3, 2, -6) | V3ω1−2ψ1+6ψ2 → (3, -2, 6) | V3ω1+2ψ1+6ψ2 → (3, 2, 6) | V4ω1 → (4, 0, 0) | V6ω1 → (6, 0, 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 | 3ω1 ω1 −ω1 −3ω1 | 3ω1 ω1 −ω1 −3ω1 | 4ω1 2ω1 0 −2ω1 −4ω1 | 6ω1 4ω1 2ω1 0 −2ω1 −4ω1 −6ω1 | ||||||||||||||||||||||||||||||||||||||||||||||
Weights of elements in (fundamental coords w.r.t. Cartan of subalgebra) + Cartan centralizer | −4ψ1 | 0 | 4ψ1 | 2ω1 0 −2ω1 | 3ω1−2ψ1−6ψ2 ω1−2ψ1−6ψ2 −ω1−2ψ1−6ψ2 −3ω1−2ψ1−6ψ2 | 3ω1+2ψ1−6ψ2 ω1+2ψ1−6ψ2 −ω1+2ψ1−6ψ2 −3ω1+2ψ1−6ψ2 | 3ω1−2ψ1+6ψ2 ω1−2ψ1+6ψ2 −ω1−2ψ1+6ψ2 −3ω1−2ψ1+6ψ2 | 3ω1+2ψ1+6ψ2 ω1+2ψ1+6ψ2 −ω1+2ψ1+6ψ2 −3ω1+2ψ1+6ψ2 | 4ω1 2ω1 0 −2ω1 −4ω1 | 6ω1 4ω1 2ω1 0 −2ω1 −4ω1 −6ω1 | ||||||||||||||||||||||||||||||||||||||||||||||
Single module character over Cartan of s.a.+ Cartan of centralizer of s.a. | M−4ψ1 | M0 | M4ψ1 | M2ω1⊕M0⊕M−2ω1 | M3ω1−2ψ1−6ψ2⊕Mω1−2ψ1−6ψ2⊕M−ω1−2ψ1−6ψ2⊕M−3ω1−2ψ1−6ψ2 | M3ω1+2ψ1−6ψ2⊕Mω1+2ψ1−6ψ2⊕M−ω1+2ψ1−6ψ2⊕M−3ω1+2ψ1−6ψ2 | M3ω1−2ψ1+6ψ2⊕Mω1−2ψ1+6ψ2⊕M−ω1−2ψ1+6ψ2⊕M−3ω1−2ψ1+6ψ2 | M3ω1+2ψ1+6ψ2⊕Mω1+2ψ1+6ψ2⊕M−ω1+2ψ1+6ψ2⊕M−3ω1+2ψ1+6ψ2 | M4ω1⊕M2ω1⊕M0⊕M−2ω1⊕M−4ω1 | M6ω1⊕M4ω1⊕M2ω1⊕M0⊕M−2ω1⊕M−4ω1⊕M−6ω1 | ||||||||||||||||||||||||||||||||||||||||||||||
Isotypic character | M−4ψ1 | 2M0 | M4ψ1 | M2ω1⊕M0⊕M−2ω1 | M3ω1−2ψ1−6ψ2⊕Mω1−2ψ1−6ψ2⊕M−ω1−2ψ1−6ψ2⊕M−3ω1−2ψ1−6ψ2 | M3ω1+2ψ1−6ψ2⊕Mω1+2ψ1−6ψ2⊕M−ω1+2ψ1−6ψ2⊕M−3ω1+2ψ1−6ψ2 | M3ω1−2ψ1+6ψ2⊕Mω1−2ψ1+6ψ2⊕M−ω1−2ψ1+6ψ2⊕M−3ω1−2ψ1+6ψ2 | M3ω1+2ψ1+6ψ2⊕Mω1+2ψ1+6ψ2⊕M−ω1+2ψ1+6ψ2⊕M−3ω1+2ψ1+6ψ2 | M4ω1⊕M2ω1⊕M0⊕M−2ω1⊕M−4ω1 | M6ω1⊕M4ω1⊕M2ω1⊕M0⊕M−2ω1⊕M−4ω1⊕M−6ω1 |