Isotypical components + highest weight | \(\displaystyle V_{2\psi_{3}-4\psi_{4}} \) → (0, 0, 0, 2, -4) | \(\displaystyle V_{-\psi_{2}+\psi_{3}-2\psi_{4}} \) → (0, 0, -1, 1, -2) | \(\displaystyle V_{-2\psi_{2}} \) → (0, 0, -2, 0, 0) | \(\displaystyle V_{\psi_{2}-2\psi_{4}} \) → (0, 0, 1, 0, -2) | \(\displaystyle V_{-\psi_{2}+2\psi_{3}-2\psi_{4}} \) → (0, 0, -1, 2, -2) | \(\displaystyle V_{-\psi_{3}} \) → (0, 0, 0, -1, 0) | \(\displaystyle V_{-2\psi_{2}+\psi_{3}} \) → (0, 0, -2, 1, 0) | \(\displaystyle V_{\psi_{2}+\psi_{3}-2\psi_{4}} \) → (0, 0, 1, 1, -2) | \(\displaystyle V_{2\psi_{2}-2\psi_{3}} \) → (0, 0, 2, -2, 0) | \(\displaystyle V_{0} \) → (0, 0, 0, 0, 0) | \(\displaystyle V_{-2\psi_{2}+2\psi_{3}} \) → (0, 0, -2, 2, 0) | \(\displaystyle V_{-\psi_{2}-\psi_{3}+2\psi_{4}} \) → (0, 0, -1, -1, 2) | \(\displaystyle V_{2\psi_{2}-\psi_{3}} \) → (0, 0, 2, -1, 0) | \(\displaystyle V_{\psi_{3}} \) → (0, 0, 0, 1, 0) | \(\displaystyle V_{\psi_{2}-2\psi_{3}+2\psi_{4}} \) → (0, 0, 1, -2, 2) | \(\displaystyle V_{-\psi_{2}+2\psi_{4}} \) → (0, 0, -1, 0, 2) | \(\displaystyle V_{2\psi_{2}} \) → (0, 0, 2, 0, 0) | \(\displaystyle V_{\psi_{2}-\psi_{3}+2\psi_{4}} \) → (0, 0, 1, -1, 2) | \(\displaystyle V_{-2\psi_{3}+4\psi_{4}} \) → (0, 0, 0, -2, 4) | \(\displaystyle V_{\omega_{1}-\psi_{1}+\psi_{3}-2\psi_{4}} \) → (1, -1, 0, 1, -2) | \(\displaystyle V_{\omega_{1}-\psi_{1}-\psi_{2}} \) → (1, -1, -1, 0, 0) | \(\displaystyle V_{\omega_{1}-\psi_{1}+\psi_{2}-\psi_{3}} \) → (1, -1, 1, -1, 0) | \(\displaystyle V_{\omega_{1}-\psi_{1}-\psi_{2}+\psi_{3}} \) → (1, -1, -1, 1, 0) | \(\displaystyle V_{\omega_{1}+\psi_{1}+\psi_{3}-2\psi_{4}} \) → (1, 1, 0, 1, -2) | \(\displaystyle V_{\omega_{1}+\psi_{1}-\psi_{2}} \) → (1, 1, -1, 0, 0) | \(\displaystyle V_{\omega_{1}-\psi_{1}+\psi_{2}} \) → (1, -1, 1, 0, 0) | \(\displaystyle V_{\omega_{1}-\psi_{1}-\psi_{3}+2\psi_{4}} \) → (1, -1, 0, -1, 2) | \(\displaystyle V_{\omega_{1}+\psi_{1}+\psi_{2}-\psi_{3}} \) → (1, 1, 1, -1, 0) | \(\displaystyle V_{\omega_{1}+\psi_{1}-\psi_{2}+\psi_{3}} \) → (1, 1, -1, 1, 0) | \(\displaystyle V_{\omega_{1}+\psi_{1}+\psi_{2}} \) → (1, 1, 1, 0, 0) | \(\displaystyle V_{\omega_{1}+\psi_{1}-\psi_{3}+2\psi_{4}} \) → (1, 1, 0, -1, 2) | \(\displaystyle V_{2\omega_{1}-2\psi_{1}} \) → (2, -2, 0, 0, 0) | \(\displaystyle V_{2\omega_{1}} \) → (2, 0, 0, 0, 0) | \(\displaystyle V_{2\omega_{1}+2\psi_{1}} \) → (2, 2, 0, 0, 0) |
Module label | \(W_{1}\) | \(W_{2}\) | \(W_{3}\) | \(W_{4}\) | \(W_{5}\) | \(W_{6}\) | \(W_{7}\) | \(W_{8}\) | \(W_{9}\) | \(W_{10}\) | \(W_{11}\) | \(W_{12}\) | \(W_{13}\) | \(W_{14}\) | \(W_{15}\) | \(W_{16}\) | \(W_{17}\) | \(W_{18}\) | \(W_{19}\) | \(W_{20}\) | \(W_{21}\) | \(W_{22}\) | \(W_{23}\) | \(W_{24}\) | \(W_{25}\) | \(W_{26}\) | \(W_{27}\) | \(W_{28}\) | \(W_{29}\) | \(W_{30}\) | \(W_{31}\) | \(W_{32}\) | \(W_{33}\) | \(W_{34}\) |
Module elements (weight vectors). In blue - corresp. F element. In red -corresp. H element. | | | | | | | | | | Cartan of centralizer component. | | | | | | | | | | | | | | | | | | | | | | \(g_{23}\) | \(-g_{-1}\) | \(-2g_{-25}\) |
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| Semisimple subalgebra component. \(-g_{24}\) | \(2h_{5}+4h_{4}+4h_{3}+4h_{2}+2h_{1}\) | \(2g_{-24}\) |
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| \(g_{25}\) | \(-g_{1}\) | \(-2g_{-23}\) |
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Weights of elements in fundamental coords w.r.t. Cartan of subalgebra in same order as above | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\omega_{1}\) \(-\omega_{1}\) | \(\omega_{1}\) \(-\omega_{1}\) | \(\omega_{1}\) \(-\omega_{1}\) | \(\omega_{1}\) \(-\omega_{1}\) | \(\omega_{1}\) \(-\omega_{1}\) | \(\omega_{1}\) \(-\omega_{1}\) | \(\omega_{1}\) \(-\omega_{1}\) | \(\omega_{1}\) \(-\omega_{1}\) | \(\omega_{1}\) \(-\omega_{1}\) | \(\omega_{1}\) \(-\omega_{1}\) | \(\omega_{1}\) \(-\omega_{1}\) | \(\omega_{1}\) \(-\omega_{1}\) | \(2\omega_{1}\) \(0\) \(-2\omega_{1}\) | \(2\omega_{1}\) \(0\) \(-2\omega_{1}\) | \(2\omega_{1}\) \(0\) \(-2\omega_{1}\) |
Weights of elements in (fundamental coords w.r.t. Cartan of subalgebra) + Cartan centralizer | \(2\psi_{3}-4\psi_{4}\) | \(-\psi_{2}+\psi_{3}-2\psi_{4}\) | \(-2\psi_{2}\) | \(\psi_{2}-2\psi_{4}\) | \(-\psi_{2}+2\psi_{3}-2\psi_{4}\) | \(-\psi_{3}\) | \(-2\psi_{2}+\psi_{3}\) | \(\psi_{2}+\psi_{3}-2\psi_{4}\) | \(2\psi_{2}-2\psi_{3}\) | \(0\) | \(-2\psi_{2}+2\psi_{3}\) | \(-\psi_{2}-\psi_{3}+2\psi_{4}\) | \(2\psi_{2}-\psi_{3}\) | \(\psi_{3}\) | \(\psi_{2}-2\psi_{3}+2\psi_{4}\) | \(-\psi_{2}+2\psi_{4}\) | \(2\psi_{2}\) | \(\psi_{2}-\psi_{3}+2\psi_{4}\) | \(-2\psi_{3}+4\psi_{4}\) | \(\omega_{1}-\psi_{1}+\psi_{3}-2\psi_{4}\) \(-\omega_{1}-\psi_{1}+\psi_{3}-2\psi_{4}\) | \(\omega_{1}-\psi_{1}-\psi_{2}\) \(-\omega_{1}-\psi_{1}-\psi_{2}\) | \(\omega_{1}-\psi_{1}+\psi_{2}-\psi_{3}\) \(-\omega_{1}-\psi_{1}+\psi_{2}-\psi_{3}\) | \(\omega_{1}-\psi_{1}-\psi_{2}+\psi_{3}\) \(-\omega_{1}-\psi_{1}-\psi_{2}+\psi_{3}\) | \(\omega_{1}+\psi_{1}+\psi_{3}-2\psi_{4}\) \(-\omega_{1}+\psi_{1}+\psi_{3}-2\psi_{4}\) | \(\omega_{1}+\psi_{1}-\psi_{2}\) \(-\omega_{1}+\psi_{1}-\psi_{2}\) | \(\omega_{1}-\psi_{1}+\psi_{2}\) \(-\omega_{1}-\psi_{1}+\psi_{2}\) | \(\omega_{1}-\psi_{1}-\psi_{3}+2\psi_{4}\) \(-\omega_{1}-\psi_{1}-\psi_{3}+2\psi_{4}\) | \(\omega_{1}+\psi_{1}+\psi_{2}-\psi_{3}\) \(-\omega_{1}+\psi_{1}+\psi_{2}-\psi_{3}\) | \(\omega_{1}+\psi_{1}-\psi_{2}+\psi_{3}\) \(-\omega_{1}+\psi_{1}-\psi_{2}+\psi_{3}\) | \(\omega_{1}+\psi_{1}+\psi_{2}\) \(-\omega_{1}+\psi_{1}+\psi_{2}\) | \(\omega_{1}+\psi_{1}-\psi_{3}+2\psi_{4}\) \(-\omega_{1}+\psi_{1}-\psi_{3}+2\psi_{4}\) | \(2\omega_{1}-2\psi_{1}\) \(-2\psi_{1}\) \(-2\omega_{1}-2\psi_{1}\) | \(2\omega_{1}\) \(0\) \(-2\omega_{1}\) | \(2\omega_{1}+2\psi_{1}\) \(2\psi_{1}\) \(-2\omega_{1}+2\psi_{1}\) |
Single module character over Cartan of s.a.+ Cartan of centralizer of s.a. | \(\displaystyle M_{2\psi_{3}-4\psi_{4}}\) | \(\displaystyle M_{-\psi_{2}+\psi_{3}-2\psi_{4}}\) | \(\displaystyle M_{-2\psi_{2}}\) | \(\displaystyle M_{\psi_{2}-2\psi_{4}}\) | \(\displaystyle M_{-\psi_{2}+2\psi_{3}-2\psi_{4}}\) | \(\displaystyle M_{-\psi_{3}}\) | \(\displaystyle M_{-2\psi_{2}+\psi_{3}}\) | \(\displaystyle M_{\psi_{2}+\psi_{3}-2\psi_{4}}\) | \(\displaystyle M_{2\psi_{2}-2\psi_{3}}\) | \(\displaystyle M_{0}\) | \(\displaystyle M_{-2\psi_{2}+2\psi_{3}}\) | \(\displaystyle M_{-\psi_{2}-\psi_{3}+2\psi_{4}}\) | \(\displaystyle M_{2\psi_{2}-\psi_{3}}\) | \(\displaystyle M_{\psi_{3}}\) | \(\displaystyle M_{\psi_{2}-2\psi_{3}+2\psi_{4}}\) | \(\displaystyle M_{-\psi_{2}+2\psi_{4}}\) | \(\displaystyle M_{2\psi_{2}}\) | \(\displaystyle M_{\psi_{2}-\psi_{3}+2\psi_{4}}\) | \(\displaystyle M_{-2\psi_{3}+4\psi_{4}}\) | \(\displaystyle M_{\omega_{1}-\psi_{1}+\psi_{3}-2\psi_{4}}\oplus M_{-\omega_{1}-\psi_{1}+\psi_{3}-2\psi_{4}}\) | \(\displaystyle M_{\omega_{1}-\psi_{1}-\psi_{2}}\oplus M_{-\omega_{1}-\psi_{1}-\psi_{2}}\) | \(\displaystyle M_{\omega_{1}-\psi_{1}+\psi_{2}-\psi_{3}}\oplus M_{-\omega_{1}-\psi_{1}+\psi_{2}-\psi_{3}}\) | \(\displaystyle M_{\omega_{1}-\psi_{1}-\psi_{2}+\psi_{3}}\oplus M_{-\omega_{1}-\psi_{1}-\psi_{2}+\psi_{3}}\) | \(\displaystyle M_{\omega_{1}+\psi_{1}+\psi_{3}-2\psi_{4}}\oplus M_{-\omega_{1}+\psi_{1}+\psi_{3}-2\psi_{4}}\) | \(\displaystyle M_{\omega_{1}+\psi_{1}-\psi_{2}}\oplus M_{-\omega_{1}+\psi_{1}-\psi_{2}}\) | \(\displaystyle M_{\omega_{1}-\psi_{1}+\psi_{2}}\oplus M_{-\omega_{1}-\psi_{1}+\psi_{2}}\) | \(\displaystyle M_{\omega_{1}-\psi_{1}-\psi_{3}+2\psi_{4}}\oplus M_{-\omega_{1}-\psi_{1}-\psi_{3}+2\psi_{4}}\) | \(\displaystyle M_{\omega_{1}+\psi_{1}+\psi_{2}-\psi_{3}}\oplus M_{-\omega_{1}+\psi_{1}+\psi_{2}-\psi_{3}}\) | \(\displaystyle M_{\omega_{1}+\psi_{1}-\psi_{2}+\psi_{3}}\oplus M_{-\omega_{1}+\psi_{1}-\psi_{2}+\psi_{3}}\) | \(\displaystyle M_{\omega_{1}+\psi_{1}+\psi_{2}}\oplus M_{-\omega_{1}+\psi_{1}+\psi_{2}}\) | \(\displaystyle M_{\omega_{1}+\psi_{1}-\psi_{3}+2\psi_{4}}\oplus M_{-\omega_{1}+\psi_{1}-\psi_{3}+2\psi_{4}}\) | \(\displaystyle M_{2\omega_{1}-2\psi_{1}}\oplus M_{-2\psi_{1}}\oplus M_{-2\omega_{1}-2\psi_{1}}\) | \(\displaystyle M_{2\omega_{1}}\oplus M_{0}\oplus M_{-2\omega_{1}}\) | \(\displaystyle M_{2\omega_{1}+2\psi_{1}}\oplus M_{2\psi_{1}}\oplus M_{-2\omega_{1}+2\psi_{1}}\) |
Isotypic character | \(\displaystyle M_{2\psi_{3}-4\psi_{4}}\) | \(\displaystyle M_{-\psi_{2}+\psi_{3}-2\psi_{4}}\) | \(\displaystyle M_{-2\psi_{2}}\) | \(\displaystyle M_{\psi_{2}-2\psi_{4}}\) | \(\displaystyle M_{-\psi_{2}+2\psi_{3}-2\psi_{4}}\) | \(\displaystyle M_{-\psi_{3}}\) | \(\displaystyle M_{-2\psi_{2}+\psi_{3}}\) | \(\displaystyle M_{\psi_{2}+\psi_{3}-2\psi_{4}}\) | \(\displaystyle M_{2\psi_{2}-2\psi_{3}}\) | \(\displaystyle 4M_{0}\) | \(\displaystyle M_{-2\psi_{2}+2\psi_{3}}\) | \(\displaystyle M_{-\psi_{2}-\psi_{3}+2\psi_{4}}\) | \(\displaystyle M_{2\psi_{2}-\psi_{3}}\) | \(\displaystyle M_{\psi_{3}}\) | \(\displaystyle M_{\psi_{2}-2\psi_{3}+2\psi_{4}}\) | \(\displaystyle M_{-\psi_{2}+2\psi_{4}}\) | \(\displaystyle M_{2\psi_{2}}\) | \(\displaystyle M_{\psi_{2}-\psi_{3}+2\psi_{4}}\) | \(\displaystyle M_{-2\psi_{3}+4\psi_{4}}\) | \(\displaystyle M_{\omega_{1}-\psi_{1}+\psi_{3}-2\psi_{4}}\oplus M_{-\omega_{1}-\psi_{1}+\psi_{3}-2\psi_{4}}\) | \(\displaystyle M_{\omega_{1}-\psi_{1}-\psi_{2}}\oplus M_{-\omega_{1}-\psi_{1}-\psi_{2}}\) | \(\displaystyle M_{\omega_{1}-\psi_{1}+\psi_{2}-\psi_{3}}\oplus M_{-\omega_{1}-\psi_{1}+\psi_{2}-\psi_{3}}\) | \(\displaystyle M_{\omega_{1}-\psi_{1}-\psi_{2}+\psi_{3}}\oplus M_{-\omega_{1}-\psi_{1}-\psi_{2}+\psi_{3}}\) | \(\displaystyle M_{\omega_{1}+\psi_{1}+\psi_{3}-2\psi_{4}}\oplus M_{-\omega_{1}+\psi_{1}+\psi_{3}-2\psi_{4}}\) | \(\displaystyle M_{\omega_{1}+\psi_{1}-\psi_{2}}\oplus M_{-\omega_{1}+\psi_{1}-\psi_{2}}\) | \(\displaystyle M_{\omega_{1}-\psi_{1}+\psi_{2}}\oplus M_{-\omega_{1}-\psi_{1}+\psi_{2}}\) | \(\displaystyle M_{\omega_{1}-\psi_{1}-\psi_{3}+2\psi_{4}}\oplus M_{-\omega_{1}-\psi_{1}-\psi_{3}+2\psi_{4}}\) | \(\displaystyle M_{\omega_{1}+\psi_{1}+\psi_{2}-\psi_{3}}\oplus M_{-\omega_{1}+\psi_{1}+\psi_{2}-\psi_{3}}\) | \(\displaystyle M_{\omega_{1}+\psi_{1}-\psi_{2}+\psi_{3}}\oplus M_{-\omega_{1}+\psi_{1}-\psi_{2}+\psi_{3}}\) | \(\displaystyle M_{\omega_{1}+\psi_{1}+\psi_{2}}\oplus M_{-\omega_{1}+\psi_{1}+\psi_{2}}\) | \(\displaystyle M_{\omega_{1}+\psi_{1}-\psi_{3}+2\psi_{4}}\oplus M_{-\omega_{1}+\psi_{1}-\psi_{3}+2\psi_{4}}\) | \(\displaystyle M_{2\omega_{1}-2\psi_{1}}\oplus M_{-2\psi_{1}}\oplus M_{-2\omega_{1}-2\psi_{1}}\) | \(\displaystyle M_{2\omega_{1}}\oplus M_{0}\oplus M_{-2\omega_{1}}\) | \(\displaystyle M_{2\omega_{1}+2\psi_{1}}\oplus M_{2\psi_{1}}\oplus M_{-2\omega_{1}+2\psi_{1}}\) |