Highest vectors of representations (total 20) ; the vectors are over the primal subalgebra. | g6+g−1 | −h4+h3 | −h6+h1 | −h5+h2 | g1+g−6 | g15 | g10 | g8 | g12 | g4 | g3 | g20 | g21 | g17 | g19 | g18 | g13 | g14 | g16 | g9 |
weight | 0 | 0 | 0 | 0 | 0 | ω1 | ω1 | ω1 | ω1 | ω2 | ω2 | 2ω1 | 2ω1 | 2ω1 | 2ω1 | ω1+ω2 | ω1+ω2 | ω1+ω2 | ω1+ω2 | 2ω2 |
weights rel. to Cartan of (centralizer+semisimple s.a.). | 2ψ2−4ψ3 | 0 | 0 | 0 | −2ψ2+4ψ3 | ω1−4ψ1−2ψ3 | ω1−4ψ1−2ψ2+2ψ3 | ω1+4ψ1+2ψ2−2ψ3 | ω1+4ψ1+2ψ3 | ω2−6ψ1+2ψ2 | ω2+6ψ1−2ψ2 | 2ω1+2ψ2−4ψ3 | 2ω1 | 2ω1 | 2ω1−2ψ2+4ψ3 | ω1+ω2+2ψ1−2ψ2−2ψ3 | ω1+ω2−2ψ1+4ψ2−2ψ3 | ω1+ω2+2ψ1−4ψ2+2ψ3 | ω1+ω2−2ψ1+2ψ2+2ψ3 | 2ω2 |
Isotypical components + highest weight | V2ψ2−4ψ3 → (0, 0, 0, 2, -4) | V0 → (0, 0, 0, 0, 0) | V−2ψ2+4ψ3 → (0, 0, 0, -2, 4) | Vω1−4ψ1−2ψ3 → (1, 0, -4, 0, -2) | Vω1−4ψ1−2ψ2+2ψ3 → (1, 0, -4, -2, 2) | Vω1+4ψ1+2ψ2−2ψ3 → (1, 0, 4, 2, -2) | Vω1+4ψ1+2ψ3 → (1, 0, 4, 0, 2) | Vω2−6ψ1+2ψ2 → (0, 1, -6, 2, 0) | Vω2+6ψ1−2ψ2 → (0, 1, 6, -2, 0) | V2ω1+2ψ2−4ψ3 → (2, 0, 0, 2, -4) | V2ω1 → (2, 0, 0, 0, 0) | V2ω1−2ψ2+4ψ3 → (2, 0, 0, -2, 4) | Vω1+ω2+2ψ1−2ψ2−2ψ3 → (1, 1, 2, -2, -2) | Vω1+ω2−2ψ1+4ψ2−2ψ3 → (1, 1, -2, 4, -2) | Vω1+ω2+2ψ1−4ψ2+2ψ3 → (1, 1, 2, -4, 2) | Vω1+ω2−2ψ1+2ψ2+2ψ3 → (1, 1, -2, 2, 2) | V2ω2 → (0, 2, 0, 0, 0) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Module label | W1 | W2 | W3 | W4 | W5 | W6 | W7 | W8 | W9 | W10 | W11 | W12 | W13 | W14 | W15 | W16 | W17 | W18 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Module elements (weight vectors). In blue - corresp. F element. In red -corresp. H element. |
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Weights of elements in fundamental coords w.r.t. Cartan of subalgebra in same order as above | 0 | 0 | 0 | ω1 −ω1 | ω1 −ω1 | ω1 −ω1 | ω1 −ω1 | ω2 −ω2 | ω2 −ω2 | 2ω1 0 −2ω1 | 2ω1 0 −2ω1 | 2ω1 0 −2ω1 | 2ω1 0 −2ω1 | ω1+ω2 −ω1+ω2 ω1−ω2 −ω1−ω2 | ω1+ω2 −ω1+ω2 ω1−ω2 −ω1−ω2 | 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 | 2ψ2−4ψ3 | 0 | −2ψ2+4ψ3 | ω1−4ψ1−2ψ3 −ω1−4ψ1−2ψ3 | ω1−4ψ1−2ψ2+2ψ3 −ω1−4ψ1−2ψ2+2ψ3 | ω1+4ψ1+2ψ2−2ψ3 −ω1+4ψ1+2ψ2−2ψ3 | ω1+4ψ1+2ψ3 −ω1+4ψ1+2ψ3 | ω2−6ψ1+2ψ2 −ω2−6ψ1+2ψ2 | ω2+6ψ1−2ψ2 −ω2+6ψ1−2ψ2 | 2ω1+2ψ2−4ψ3 2ψ2−4ψ3 −2ω1+2ψ2−4ψ3 | 2ω1 0 −2ω1 | 2ω1 0 −2ω1 | 2ω1−2ψ2+4ψ3 −2ψ2+4ψ3 −2ω1−2ψ2+4ψ3 | ω1+ω2+2ψ1−2ψ2−2ψ3 −ω1+ω2+2ψ1−2ψ2−2ψ3 ω1−ω2+2ψ1−2ψ2−2ψ3 −ω1−ω2+2ψ1−2ψ2−2ψ3 | ω1+ω2−2ψ1+4ψ2−2ψ3 −ω1+ω2−2ψ1+4ψ2−2ψ3 ω1−ω2−2ψ1+4ψ2−2ψ3 −ω1−ω2−2ψ1+4ψ2−2ψ3 | ω1+ω2+2ψ1−4ψ2+2ψ3 −ω1+ω2+2ψ1−4ψ2+2ψ3 ω1−ω2+2ψ1−4ψ2+2ψ3 −ω1−ω2+2ψ1−4ψ2+2ψ3 | ω1+ω2−2ψ1+2ψ2+2ψ3 −ω1+ω2−2ψ1+2ψ2+2ψ3 ω1−ω2−2ψ1+2ψ2+2ψ3 −ω1−ω2−2ψ1+2ψ2+2ψ3 | 2ω2 0 −2ω2 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Single module character over Cartan of s.a.+ Cartan of centralizer of s.a. | M2ψ2−4ψ3 | M0 | M−2ψ2+4ψ3 | Mω1−4ψ1−2ψ3⊕M−ω1−4ψ1−2ψ3 | Mω1−4ψ1−2ψ2+2ψ3⊕M−ω1−4ψ1−2ψ2+2ψ3 | Mω1+4ψ1+2ψ2−2ψ3⊕M−ω1+4ψ1+2ψ2−2ψ3 | Mω1+4ψ1+2ψ3⊕M−ω1+4ψ1+2ψ3 | Mω2−6ψ1+2ψ2⊕M−ω2−6ψ1+2ψ2 | Mω2+6ψ1−2ψ2⊕M−ω2+6ψ1−2ψ2 | M2ω1+2ψ2−4ψ3⊕M2ψ2−4ψ3⊕M−2ω1+2ψ2−4ψ3 | M2ω1⊕M0⊕M−2ω1 | M2ω1⊕M0⊕M−2ω1 | M2ω1−2ψ2+4ψ3⊕M−2ψ2+4ψ3⊕M−2ω1−2ψ2+4ψ3 | Mω1+ω2+2ψ1−2ψ2−2ψ3⊕M−ω1+ω2+2ψ1−2ψ2−2ψ3⊕Mω1−ω2+2ψ1−2ψ2−2ψ3⊕M−ω1−ω2+2ψ1−2ψ2−2ψ3 | Mω1+ω2−2ψ1+4ψ2−2ψ3⊕M−ω1+ω2−2ψ1+4ψ2−2ψ3⊕Mω1−ω2−2ψ1+4ψ2−2ψ3⊕M−ω1−ω2−2ψ1+4ψ2−2ψ3 | Mω1+ω2+2ψ1−4ψ2+2ψ3⊕M−ω1+ω2+2ψ1−4ψ2+2ψ3⊕Mω1−ω2+2ψ1−4ψ2+2ψ3⊕M−ω1−ω2+2ψ1−4ψ2+2ψ3 | Mω1+ω2−2ψ1+2ψ2+2ψ3⊕M−ω1+ω2−2ψ1+2ψ2+2ψ3⊕Mω1−ω2−2ψ1+2ψ2+2ψ3⊕M−ω1−ω2−2ψ1+2ψ2+2ψ3 | M2ω2⊕M0⊕M−2ω2 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Isotypic character | M2ψ2−4ψ3 | 3M0 | M−2ψ2+4ψ3 | Mω1−4ψ1−2ψ3⊕M−ω1−4ψ1−2ψ3 | Mω1−4ψ1−2ψ2+2ψ3⊕M−ω1−4ψ1−2ψ2+2ψ3 | Mω1+4ψ1+2ψ2−2ψ3⊕M−ω1+4ψ1+2ψ2−2ψ3 | Mω1+4ψ1+2ψ3⊕M−ω1+4ψ1+2ψ3 | Mω2−6ψ1+2ψ2⊕M−ω2−6ψ1+2ψ2 | Mω2+6ψ1−2ψ2⊕M−ω2+6ψ1−2ψ2 | M2ω1+2ψ2−4ψ3⊕M2ψ2−4ψ3⊕M−2ω1+2ψ2−4ψ3 | M2ω1⊕M0⊕M−2ω1 | M2ω1⊕M0⊕M−2ω1 | M2ω1−2ψ2+4ψ3⊕M−2ψ2+4ψ3⊕M−2ω1−2ψ2+4ψ3 | Mω1+ω2+2ψ1−2ψ2−2ψ3⊕M−ω1+ω2+2ψ1−2ψ2−2ψ3⊕Mω1−ω2+2ψ1−2ψ2−2ψ3⊕M−ω1−ω2+2ψ1−2ψ2−2ψ3 | Mω1+ω2−2ψ1+4ψ2−2ψ3⊕M−ω1+ω2−2ψ1+4ψ2−2ψ3⊕Mω1−ω2−2ψ1+4ψ2−2ψ3⊕M−ω1−ω2−2ψ1+4ψ2−2ψ3 | Mω1+ω2+2ψ1−4ψ2+2ψ3⊕M−ω1+ω2+2ψ1−4ψ2+2ψ3⊕Mω1−ω2+2ψ1−4ψ2+2ψ3⊕M−ω1−ω2+2ψ1−4ψ2+2ψ3 | Mω1+ω2−2ψ1+2ψ2+2ψ3⊕M−ω1+ω2−2ψ1+2ψ2+2ψ3⊕Mω1−ω2−2ψ1+2ψ2+2ψ3⊕M−ω1−ω2−2ψ1+2ψ2+2ψ3 | M2ω2⊕M0⊕M−2ω2 |