Highest vectors of representations (total 9) ; the vectors are over the primal subalgebra. | −h5−2h4+2h2+h1 | g9+1/3g8 | g11+3/4g5+3/4g1 | g3 | g7+3g6 | g12 | g14+g13 | g10 | g15 |
weight | 0 | 2ω1 | 2ω1 | 2ω1 | 2ω1 | 4ω1 | 4ω1 | 4ω1 | 6ω1 |
weights rel. to Cartan of (centralizer+semisimple s.a.). | 0 | 2ω1−6ψ | 2ω1 | 2ω1 | 2ω1+6ψ | 4ω1−6ψ | 4ω1 | 4ω1+6ψ | 6ω1 |
Isotypical components + highest weight | V0 → (0, 0) | V2ω1−6ψ → (2, -6) | V2ω1 → (2, 0) | V2ω1+6ψ → (2, 6) | V4ω1−6ψ → (4, -6) | V4ω1 → (4, 0) | V4ω1+6ψ → (4, 6) | V6ω1 → (6, 0) | |||||||||||||||||||||||||||||||||||||||||||||
Module label | W1 | W2 | W3 | W4 | W5 | W6 | W7 | W8 | W9 | ||||||||||||||||||||||||||||||||||||||||||||
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 | 2ω1 0 −2ω1 | 2ω1 0 −2ω1 | 2ω1 0 −2ω1 | 2ω1 0 −2ω1 | 4ω1 2ω1 0 −2ω1 −4ω1 | 4ω1 2ω1 0 −2ω1 −4ω1 | 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 | 0 | 2ω1−6ψ −6ψ −2ω1−6ψ | 2ω1 0 −2ω1 | 2ω1 0 −2ω1 | 2ω1+6ψ 6ψ −2ω1+6ψ | 4ω1−6ψ 2ω1−6ψ −6ψ −2ω1−6ψ −4ω1−6ψ | 4ω1 2ω1 0 −2ω1 −4ω1 | 4ω1+6ψ 2ω1+6ψ 6ψ −2ω1+6ψ −4ω1+6ψ | 6ω1 4ω1 2ω1 0 −2ω1 −4ω1 −6ω1 | ||||||||||||||||||||||||||||||||||||||||||||
Single module character over Cartan of s.a.+ Cartan of centralizer of s.a. | M0 | M2ω1−6ψ⊕M−6ψ⊕M−2ω1−6ψ | M2ω1⊕M0⊕M−2ω1 | M2ω1⊕M0⊕M−2ω1 | M2ω1+6ψ⊕M6ψ⊕M−2ω1+6ψ | M4ω1−6ψ⊕M2ω1−6ψ⊕M−6ψ⊕M−2ω1−6ψ⊕M−4ω1−6ψ | M4ω1⊕M2ω1⊕M0⊕M−2ω1⊕M−4ω1 | M4ω1+6ψ⊕M2ω1+6ψ⊕M6ψ⊕M−2ω1+6ψ⊕M−4ω1+6ψ | M6ω1⊕M4ω1⊕M2ω1⊕M0⊕M−2ω1⊕M−4ω1⊕M−6ω1 | ||||||||||||||||||||||||||||||||||||||||||||
Isotypic character | M0 | M2ω1−6ψ⊕M−6ψ⊕M−2ω1−6ψ | M2ω1⊕M0⊕M−2ω1 | M2ω1⊕M0⊕M−2ω1 | M2ω1+6ψ⊕M6ψ⊕M−2ω1+6ψ | M4ω1−6ψ⊕M2ω1−6ψ⊕M−6ψ⊕M−2ω1−6ψ⊕M−4ω1−6ψ | M4ω1⊕M2ω1⊕M0⊕M−2ω1⊕M−4ω1 | M4ω1+6ψ⊕M2ω1+6ψ⊕M6ψ⊕M−2ω1+6ψ⊕M−4ω1+6ψ | M6ω1⊕M4ω1⊕M2ω1⊕M0⊕M−2ω1⊕M−4ω1⊕M−6ω1 |
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