"Elements of finite order (EFO) in Lie groups"의 두 판 사이의 차이
둘러보기로 가기
검색하러 가기
imported>Pythagoras0 |
imported>Pythagoras0 |
||
| 8번째 줄: | 8번째 줄: | ||
===$U(n)$=== | ===$U(n)$=== | ||
* $N(G,m)= {n+m-1\choose m-1}$ | * $N(G,m)= {n+m-1\choose m-1}$ | ||
| + | * $N(G,m,s)=\frac{s}{n}{n\choose s}{m\choose s}$ | ||
===$SU(n)$=== | ===$SU(n)$=== | ||
* $N(G,m)= \frac{1}{m}{n+m-1\choose m-1}$ if $(n,m)=1$ | * $N(G,m)= \frac{1}{m}{n+m-1\choose m-1}$ if $(n,m)=1$ | ||
| + | * $N(G,m,s)= \frac{s}{nm}{n\choose s}{m\choose s}$ if $(n,m)=1$ | ||
==related items== | ==related items== | ||
2013년 2월 11일 (월) 13:52 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
$U(n)$
- $N(G,m)= {n+m-1\choose m-1}$
- $N(G,m,s)=\frac{s}{n}{n\choose s}{m\choose s}$
$SU(n)$
- $N(G,m)= \frac{1}{m}{n+m-1\choose m-1}$ if $(n,m)=1$
- $N(G,m,s)= \frac{s}{nm}{n\choose s}{m\choose s}$ if $(n,m)=1$