## Reduction formula for point group C_{3v}

**Characters of input representation**
E |
2C_{3} (z) |
3_{v} |

7 |
1 |
3 |

**Decomposition into Irreducible representations**
A_{1} |
A_{2} |
E |

3 |
0 |
2 |

### Symmetric Powers of Representation

**Characters of symmetric powers**
Tensor Order |
E |
2C_{3} (z) |
3_{v} |

1 |
7 |
1 |
3 |

2 |
28 |
1 |
8 |

3 |
84 |
3 |
16 |

4 |
210 |
3 |
30 |

5 |
462 |
3 |
50 |

6 |
924 |
6 |
80 |

**Decomposition into Irreducible representations**
Tensor Order |
A_{1} |
A_{2} |
E |

1 |
3 |
0 |
2 |

2 |
9 |
1 |
9 |

3 |
23 |
7 |
27 |

4 |
51 |
21 |
69 |

5 |
103 |
53 |
153 |

6 |
196 |
116 |
306 |

### Antisymmetric Powers of Representation

**Characters of antisymmetric powers**
Tensor Order |
E |
2C_{3} (z) |
3_{v} |

1 | 7 |
1 |
3 |

2 | 21 |
0 |
1 |

3 | 35 |
2 |
-5 |

4
| 35 |
2 |
-5 |

5
| 21 |
0 |
1 |

6
| 7 |
1 |
3 |

**Decomposition into Irreducible representations**
Tensor Order |
A_{1} |
A_{2} |
E |

1
| 3 |
0 |
2 |

2
| 4 |
3 |
7 |

3
| 4 |
9 |
11 |

4
| 4 |
9 |
11 |

5
| 4 |
3 |
7 |

6
| 3 |
0 |
2 |

Last update Mai, 23^{rd} 2018 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement