"Elements of finite order (EFO) in Lie groups"의 두 판 사이의 차이
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imported>Pythagoras0 |
imported>Pythagoras0 |
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| 1번째 줄: | 1번째 줄: | ||
| + | ==introduction== | ||
| + | * explicit formulas for the number of conjugacy classes of EFOs in Lie groups | ||
| + | * appears for the number of certain vacua in the quantum moduli space of M-theory compactifications on manifolds of $G_2$ holonomy | ||
| + | * $N(G,m)$ : number of conjugacy classes of $G$ in $E(G,m)$ | ||
| + | |||
| + | |||
| + | ==EFO in unitary groups== | ||
| + | ===$U(n)$=== | ||
| + | * $N(G,m)= {n+m-1\choose m-1}$ | ||
| + | |||
| + | ===$SU(n)$=== | ||
| + | * $N(G,m)= \frac{1}{m}{n+m-1\choose m-1}$ | ||
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==related items== | ==related items== | ||
* [[simple Lie groups and the Legendre symbol]] | * [[simple Lie groups and the Legendre symbol]] | ||
| − | + | * {{수학노트|url=중복조합의_공식_H(n,r)%3DC(n%2Br-1,r)}} | |
2013년 2월 11일 (월) 12:51 판
introduction
- explicit formulas for the number of conjugacy classes of EFOs in Lie groups
- appears for the number of certain vacua in the quantum moduli space of M-theory compactifications on manifolds of $G_2$ holonomy
- $N(G,m)$ : number of conjugacy classes of $G$ in $E(G,m)$
EFO in unitary groups
$U(n)$
- $N(G,m)= {n+m-1\choose m-1}$
$SU(n)$
- $N(G,m)= \frac{1}{m}{n+m-1\choose m-1}$