Highest vectors of representations (total 6) ; the vectors are over the primal subalgebra. | −h6−2h5−2/3h4+2/3h3+2h2+h1 | g20+g19 | g17 | g14 | g8 | g3 |
weight | 0 | ω1 | 2ω2 | ω2+ω3 | ω2+ω4 | ω3+ω4 |
weights rel. to Cartan of (centralizer+semisimple s.a.). | 0 | ω1 | 2ω2 | ω2+ω3−14ψ | ω2+ω4+14ψ | ω3+ω4 |
Isotypical components + highest weight | V0 → (0, 0, 0, 0, 0) | Vω1 → (1, 0, 0, 0, 0) | V2ω2 → (0, 2, 0, 0, 0) | Vω2+ω3−14ψ → (0, 1, 1, 0, -14) | Vω2+ω4+14ψ → (0, 1, 0, 1, 14) | Vω3+ω4 → (0, 0, 1, 1, 0) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||
Module label | W1 | W2 | W3 | W4 | W5 | W6 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||
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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| 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 | ω1 −ω1+2ω2 0 ω1−2ω2 −ω1 | 2ω2 ω1 −ω1+2ω2 2ω1−2ω2 0 0 −2ω1+2ω2 ω1−2ω2 −ω1 −2ω2 | ω2+ω3 ω1−ω2+ω3 ω2−ω3+ω4 −ω1+ω2+ω3 ω1−ω2−ω3+ω4 ω2−ω4 −ω2+ω3 −ω1+ω2−ω3+ω4 ω1−ω2−ω4 −ω2−ω3+ω4 −ω1+ω2−ω4 −ω2−ω4 | ω2+ω4 ω1−ω2+ω4 ω2+ω3−ω4 −ω1+ω2+ω4 ω1−ω2+ω3−ω4 ω2−ω3 −ω2+ω4 −ω1+ω2+ω3−ω4 ω1−ω2−ω3 −ω2+ω3−ω4 −ω1+ω2−ω3 −ω2−ω3 | ω3+ω4 −ω3+2ω4 2ω3−ω4 0 0 −2ω3+ω4 ω3−2ω4 −ω3−ω4 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||
Weights of elements in (fundamental coords w.r.t. Cartan of subalgebra) + Cartan centralizer | 0 | ω1 −ω1+2ω2 0 ω1−2ω2 −ω1 | 2ω2 ω1 −ω1+2ω2 2ω1−2ω2 0 0 −2ω1+2ω2 ω1−2ω2 −ω1 −2ω2 | ω2+ω3−14ψ ω1−ω2+ω3−14ψ ω2−ω3+ω4−14ψ −ω1+ω2+ω3−14ψ ω1−ω2−ω3+ω4−14ψ ω2−ω4−14ψ −ω2+ω3−14ψ −ω1+ω2−ω3+ω4−14ψ ω1−ω2−ω4−14ψ −ω2−ω3+ω4−14ψ −ω1+ω2−ω4−14ψ −ω2−ω4−14ψ | ω2+ω4+14ψ ω1−ω2+ω4+14ψ ω2+ω3−ω4+14ψ −ω1+ω2+ω4+14ψ ω1−ω2+ω3−ω4+14ψ ω2−ω3+14ψ −ω2+ω4+14ψ −ω1+ω2+ω3−ω4+14ψ ω1−ω2−ω3+14ψ −ω2+ω3−ω4+14ψ −ω1+ω2−ω3+14ψ −ω2−ω3+14ψ | ω3+ω4 −ω3+2ω4 2ω3−ω4 0 0 −2ω3+ω4 ω3−2ω4 −ω3−ω4 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||
Single module character over Cartan of s.a.+ Cartan of centralizer of s.a. | M0 | M−ω1+2ω2⊕Mω1⊕M0⊕M−ω1⊕Mω1−2ω2 | M2ω2⊕M−ω1+2ω2⊕Mω1⊕M−2ω1+2ω2⊕2M0⊕M2ω1−2ω2⊕M−ω1⊕Mω1−2ω2⊕M−2ω2 | Mω2+ω3−14ψ⊕Mω2−ω3+ω4−14ψ⊕M−ω1+ω2+ω3−14ψ⊕Mω1−ω2+ω3−14ψ⊕M−ω1+ω2−ω3+ω4−14ψ⊕Mω1−ω2−ω3+ω4−14ψ⊕M−ω2+ω3−14ψ⊕Mω2−ω4−14ψ⊕M−ω2−ω3+ω4−14ψ⊕M−ω1+ω2−ω4−14ψ⊕Mω1−ω2−ω4−14ψ⊕M−ω2−ω4−14ψ | Mω2+ω4+14ψ⊕M−ω1+ω2+ω4+14ψ⊕Mω1−ω2+ω4+14ψ⊕Mω2+ω3−ω4+14ψ⊕M−ω2+ω4+14ψ⊕Mω2−ω3+14ψ⊕M−ω1+ω2+ω3−ω4+14ψ⊕Mω1−ω2+ω3−ω4+14ψ⊕M−ω1+ω2−ω3+14ψ⊕Mω1−ω2−ω3+14ψ⊕M−ω2+ω3−ω4+14ψ⊕M−ω2−ω3+14ψ | Mω3+ω4⊕M−ω3+2ω4⊕M2ω3−ω4⊕2M0⊕M−2ω3+ω4⊕Mω3−2ω4⊕M−ω3−ω4 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||
Isotypic character | M0 | M−ω1+2ω2⊕Mω1⊕M0⊕M−ω1⊕Mω1−2ω2 | M2ω2⊕M−ω1+2ω2⊕Mω1⊕M−2ω1+2ω2⊕2M0⊕M2ω1−2ω2⊕M−ω1⊕Mω1−2ω2⊕M−2ω2 | Mω2+ω3−14ψ⊕Mω2−ω3+ω4−14ψ⊕M−ω1+ω2+ω3−14ψ⊕Mω1−ω2+ω3−14ψ⊕M−ω1+ω2−ω3+ω4−14ψ⊕Mω1−ω2−ω3+ω4−14ψ⊕M−ω2+ω3−14ψ⊕Mω2−ω4−14ψ⊕M−ω2−ω3+ω4−14ψ⊕M−ω1+ω2−ω4−14ψ⊕Mω1−ω2−ω4−14ψ⊕M−ω2−ω4−14ψ | Mω2+ω4+14ψ⊕M−ω1+ω2+ω4+14ψ⊕Mω1−ω2+ω4+14ψ⊕Mω2+ω3−ω4+14ψ⊕M−ω2+ω4+14ψ⊕Mω2−ω3+14ψ⊕M−ω1+ω2+ω3−ω4+14ψ⊕Mω1−ω2+ω3−ω4+14ψ⊕M−ω1+ω2−ω3+14ψ⊕Mω1−ω2−ω3+14ψ⊕M−ω2+ω3−ω4+14ψ⊕M−ω2−ω3+14ψ | Mω3+ω4⊕M−ω3+2ω4⊕M2ω3−ω4⊕2M0⊕M−2ω3+ω4⊕Mω3−2ω4⊕M−ω3−ω4 |