"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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* $N(G,m)= \frac{1}{m}{n+m-1\choose m-1}$ 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 $(n,m)=1$ | * $N(G,m,s)= \frac{s}{nm}{n\choose s}{m\choose s}$ if $(n,m)=1$ | ||
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==related items== | ==related items== | ||
| 22번째 줄: | 23번째 줄: | ||
* https://docs.google.com/file/d/0B8XXo8Tve1cxLU5vUzJRQUNGdnc/edit | * https://docs.google.com/file/d/0B8XXo8Tve1cxLU5vUzJRQUNGdnc/edit | ||
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| + | ==questions== | ||
| + | * http://mathoverflow.net/questions/86499/representations-of-quantum-groups-at-roots-of-unity | ||
[[분류:Q-system]] | [[분류:Q-system]] | ||
2013년 3월 9일 (토) 07:13 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 $(n,m)=1$
computational resource