Highest vectors of representations (total 4) ; the vectors are over the primal subalgebra. | g6 | g7 | g2 | g9 |
weight | 2ω1 | 2ω2 | 2ω3 | 2ω1+ω2+ω3 |
Isotypical components + highest weight | V2ω1 → (2, 0, 0) | V2ω2 → (0, 2, 0) | V2ω3 → (0, 0, 2) | V2ω1+ω2+ω3 → (2, 1, 1) | |||||||||||||||||||||||||
Module label | W1 | W2 | W3 | W4 | |||||||||||||||||||||||||
Module elements (weight vectors). In blue - corresp. F element. In red -corresp. H element. | Semisimple subalgebra component.
| Semisimple subalgebra component.
| Semisimple subalgebra component.
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Weights of elements in fundamental coords w.r.t. Cartan of subalgebra in same order as above | 2ω1 0 −2ω1 | 2ω2 0 −2ω2 | 2ω3 0 −2ω3 | 2ω1+ω2+ω3 ω2+ω3 2ω1−ω2+ω3 2ω1+ω2−ω3 −2ω1+ω2+ω3 −ω2+ω3 ω2−ω3 2ω1−ω2−ω3 −2ω1−ω2+ω3 −2ω1+ω2−ω3 −ω2−ω3 −2ω1−ω2−ω3 | |||||||||||||||||||||||||
Weights of elements in (fundamental coords w.r.t. Cartan of subalgebra) + Cartan centralizer | 2ω1 0 −2ω1 | 2ω2 0 −2ω2 | 2ω3 0 −2ω3 | 2ω1+ω2+ω3 ω2+ω3 2ω1−ω2+ω3 2ω1+ω2−ω3 −2ω1+ω2+ω3 −ω2+ω3 ω2−ω3 2ω1−ω2−ω3 −2ω1−ω2+ω3 −2ω1+ω2−ω3 −ω2−ω3 −2ω1−ω2−ω3 | |||||||||||||||||||||||||
Single module character over Cartan of s.a.+ Cartan of centralizer of s.a. | M2ω1⊕M0⊕M−2ω1 | M2ω2⊕M0⊕M−2ω2 | M2ω3⊕M0⊕M−2ω3 | M2ω1+ω2+ω3⊕Mω2+ω3⊕M2ω1−ω2+ω3⊕M2ω1+ω2−ω3⊕M−2ω1+ω2+ω3⊕M−ω2+ω3⊕Mω2−ω3⊕M2ω1−ω2−ω3⊕M−2ω1−ω2+ω3⊕M−2ω1+ω2−ω3⊕M−ω2−ω3⊕M−2ω1−ω2−ω3 | |||||||||||||||||||||||||
Isotypic character | M2ω1⊕M0⊕M−2ω1 | M2ω2⊕M0⊕M−2ω2 | M2ω3⊕M0⊕M−2ω3 | M2ω1+ω2+ω3⊕Mω2+ω3⊕M2ω1−ω2+ω3⊕M2ω1+ω2−ω3⊕M−2ω1+ω2+ω3⊕M−ω2+ω3⊕Mω2−ω3⊕M2ω1−ω2−ω3⊕M−2ω1−ω2+ω3⊕M−2ω1+ω2−ω3⊕M−ω2−ω3⊕M−2ω1−ω2−ω3 |