"Elements of finite order (EFO) in Lie groups"의 두 판 사이의 차이
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* appears for the number of certain vacua in the quantum moduli space of M-theory compactifications on manifolds of $G_2$ holonomy | * 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 $E(G,m)$ | * $N(G,m)$ : number of conjugacy classes of $G$ in $E(G,m)$ | ||
| − | + | * $N(G,m,s)$ : number of conjugacy classes of $G$ in $E(G,m,s)$ | |
==EFO in unitary groups== | ==EFO in unitary groups== | ||
2013년 2월 11일 (월) 13:47 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 $E(G,m)$
- $N(G,m,s)$ : number of conjugacy classes of $G$ in $E(G,m,s)$
EFO in unitary groups
$U(n)$
- $N(G,m)= {n+m-1\choose m-1}$
$SU(n)$
- $N(G,m)= \frac{1}{m}{n+m-1\choose m-1}$ if $(n,m)=1$