"Umbral moonshine"의 두 판 사이의 차이
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imported>Pythagoras0 |
imported>Pythagoras0 |
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| 9번째 줄: | 9번째 줄: | ||
** $\rm{PSL}(2,\mathbb{F}_p)\subset M_{24}$ | ** $\rm{PSL}(2,\mathbb{F}_p)\subset M_{24}$ | ||
* [[Mathieu moonshine]] corresponds to $k=1$ case | * [[Mathieu moonshine]] corresponds to $k=1$ case | ||
| + | * $k=2$ moonshine with $2.M_{12}$ | ||
2013년 8월 5일 (월) 02:05 판
introduction
- $k\in \{1,2,3,4,6,8\}$ or $\ell=k+1\in \{2,3,4,5,7,9\}$
$$ \frac{24}{\ell-1}-1\in \{23,11,7,5,3,2\} $$
- properties
- primes dividing $|M_{24}|$
- $(p+1)|24$
- $\rm{PSL}(2,\mathbb{F}_p)\subset M_{24}$
- Mathieu moonshine corresponds to $k=1$ case
- $k=2$ moonshine with $2.M_{12}$
Jacobi form
$\mathcal{N}=4$ super conformal algebra
- $c=6k$, $k\in \mathbb{Z}_{\geq 1}$
- two types of representations : BPS and non-BPS
extremal Jacobi forms
mock modular form
umbral forms
umbral groups
umbral moonshine conjecture
- Quantum black holes, wall crossing and mock modular forms
- Mathieu moonshine
- monstrous moonshine
- Characters of superconformal algebra and mock theta functions
computational resource