Highest vectors of representations (total 5) ; the vectors are over the primal subalgebra. | −h3+h1 | g6 | g5 | g4 | g2 |
weight | 0 | 2ω1 | ω1+ω2 | ω1+ω2 | 2ω2 |
weights rel. to Cartan of (centralizer+semisimple s.a.). | 0 | 2ω1 | ω1+ω2−4ψ | ω1+ω2+4ψ | 2ω2 |
Isotypical components + highest weight | V0 → (0, 0, 0) | V2ω1 → (2, 0, 0) | Vω1+ω2−4ψ → (1, 1, -4) | Vω1+ω2+4ψ → (1, 1, 4) | V2ω2 → (0, 2, 0) | ||||||||||||||||||||
Module label | W1 | W2 | W3 | W4 | W5 | ||||||||||||||||||||
Module elements (weight vectors). In blue - corresp. F element. In red -corresp. H element. | Cartan of centralizer component.
| Semisimple subalgebra 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 | 2ω1 0 −2ω1 | ω1+ω2 −ω1+ω2 ω1−ω2 −ω1−ω2 | ω1+ω2 −ω1+ω2 ω1−ω2 −ω1−ω2 | 2ω2 0 −2ω2 | ||||||||||||||||||||
Weights of elements in (fundamental coords w.r.t. Cartan of subalgebra) + Cartan centralizer | 0 | 2ω1 0 −2ω1 | ω1+ω2−4ψ −ω1+ω2−4ψ ω1−ω2−4ψ −ω1−ω2−4ψ | ω1+ω2+4ψ −ω1+ω2+4ψ ω1−ω2+4ψ −ω1−ω2+4ψ | 2ω2 0 −2ω2 | ||||||||||||||||||||
Single module character over Cartan of s.a.+ Cartan of centralizer of s.a. | M0 | M2ω1⊕M0⊕M−2ω1 | Mω1+ω2−4ψ⊕M−ω1+ω2−4ψ⊕Mω1−ω2−4ψ⊕M−ω1−ω2−4ψ | Mω1+ω2+4ψ⊕M−ω1+ω2+4ψ⊕Mω1−ω2+4ψ⊕M−ω1−ω2+4ψ | M2ω2⊕M0⊕M−2ω2 | ||||||||||||||||||||
Isotypic character | M0 | M2ω1⊕M0⊕M−2ω1 | Mω1+ω2−4ψ⊕M−ω1+ω2−4ψ⊕Mω1−ω2−4ψ⊕M−ω1−ω2−4ψ | Mω1+ω2+4ψ⊕M−ω1+ω2+4ψ⊕Mω1−ω2+4ψ⊕M−ω1−ω2+4ψ | M2ω2⊕M0⊕M−2ω2 |