Oh Groupe Ponctuel
non abélien, 10(20) représentations irréductiblesTable de caractères pour le groupe ponctuel Oh
| E | 8C3 | 6C2 | 6C4 | 3C2 =(C4)2 | i | 6S4 | 8S6 | 3σh | 6σd | linear, rotations | quadratic | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| A1g | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | x2+y2+z2 | |
| A2g | 1 | 1 | -1 | -1 | 1 | 1 | -1 | 1 | 1 | -1 | ||
| Eg | 2 | -1 | 0 | 0 | 2 | 2 | 0 | -1 | 2 | 0 | (2z2-x2-y2, x2-y2) | |
| T1g | 3 | 0 | -1 | 1 | -1 | 3 | 1 | 0 | -1 | -1 | (Rx, Ry, Rz) | |
| T2g | 3 | 0 | 1 | -1 | -1 | 3 | -1 | 0 | -1 | 1 | (xz, yz, xy) | |
| A1u | 1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | -1 | ||
| A2u | 1 | 1 | -1 | -1 | 1 | -1 | 1 | -1 | -1 | 1 | ||
| Eu | 2 | -1 | 0 | 0 | 2 | -2 | 0 | 1 | -2 | 0 | ||
| T1u | 3 | 0 | -1 | 1 | -1 | -3 | -1 | 0 | 1 | 1 | (x, y, z) | |
| T2u | 3 | 0 | 1 | -1 | -1 | -3 | 1 | 0 | 1 | -1 |
Table des produits pour Oh groupe ponctuel
| A1g | A2g | Eg | T1g | T2g | A1u | A2u | Eu | T1u | T2u | |
|---|---|---|---|---|---|---|---|---|---|---|
| A1g | A1g | A2g | Eg | T1g | T2g | A1u | A2u | Eu | T1u | T2u |
| A2g | A2g | A1g | Eg | T2g | T1g | A2u | A1u | Eu | T2u | T1u |
| Eg | Eg | Eg | A1g+A2g+Eg | T1g+T2g | T1g+T2g | Eu | Eu | A1u+A2u+Eu | T1u+T2u | T1u+T2u |
| T1g | T1g | T2g | T1g+T2g | A1g+Eg+T1g+T2g | A2g+Eg+T1g+T2g | T1u | T2u | T1u+T2u | A1u+Eu+T1u+T2u | A2u+Eu+T1u+T2u |
| T2g | T2g | T1g | T1g+T2g | A2g+Eg+T1g+T2g | A1g+Eg+T1g+T2g | T2u | T1u | T1u+T2u | A2u+Eu+T1u+T2u | A1u+Eu+T1u+T2u |
| A1u | A1u | A2u | Eu | T1u | T2u | A1g | A2g | Eg | T1g | T2g |
| A2u | A2u | A1u | Eu | T2u | T1u | A2g | A1g | Eg | T2g | T1g |
| Eu | Eu | Eu | A1u+A2u+Eu | T1u+T2u | T1u+T2u | Eg | Eg | A1g+A2g+Eg | T1g+T2g | T1g+T2g |
| T1u | T1u | T2u | T1u+T2u | A1u+Eu+T1u+T2u | A2u+Eu+T1u+T2u | T1g | T2g | T1g+T2g | A1g+Eg+T1g+T2g | A2g+Eg+T1g+T2g |
| T2u | T2u | T1u | T1u+T2u | A2u+Eu+T1u+T2u | A1u+Eu+T1u+T2u | T2g | T1g | T1g+T2g | A2g+Eg+T1g+T2g | A1g+Eg+T1g+T2g |
| C1 | Cs | Ci | ||
| C2 | C3 | C4 | C5 | C6 |
| C2v | C3v | C4v | C5v | C6v |
| C2h | C3h | C4h | C5h | C6h |
| D2 | D3 | D4 | D5 | D6 |
| D2h | D3h | D4h | D5h | D6h |
| D2d | D3d | D4d | D5d | D6d |
| S4 | S6 | S8 | S10 | |
| Td | Oh | Ih | ||
| C∞v | D∞h |
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