"Umbral moonshine"의 두 판 사이의 차이
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imported>Pythagoras0 |
imported>Pythagoras0 |
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| 1번째 줄: | 1번째 줄: | ||
==introduction== | ==introduction== | ||
| − | * $k | + | * $k\in \{1,2,3,4,6,8\}$ 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 | * [[Mathieu moonshine]] corresponds to $k=1$ case | ||
| 6번째 줄: | 13번째 줄: | ||
==Jacobi form== | ==Jacobi form== | ||
| − | + | * [[Jacobi forms]] | |
| 37번째 줄: | 44번째 줄: | ||
* [[monstrous moonshine]] | * [[monstrous moonshine]] | ||
* [[Characters of superconformal algebra and mock theta functions]] | * [[Characters of superconformal algebra and mock theta functions]] | ||
| + | |||
| + | |||
| + | ==computational resource== | ||
| + | * https://docs.google.com/file/d/0B8XXo8Tve1cxNW5LZDU3eGU0aVk/edit | ||
| + | |||
| + | |||
==expositions== | ==expositions== | ||
2013년 8월 5일 (월) 03:03 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
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