"Nekrasov-Okounkov hook length formula"의 두 판 사이의 차이
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imported>Pythagoras0 (새 문서: ==memo== * http://mathoverflow.net/questions/200951/nekrasov-okounkov-hook-length-formula ==articles== * Han, Guo-Niu. ‘The Nekrasov-Okounkov Hook Length Formula: Refinement, Elem...) |
imported>Pythagoras0 |
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| 1번째 줄: | 1번째 줄: | ||
| + | ==introduction== | ||
| + | * expansion formula for the powers of the Euler Product in terms of partition hook lengths, discovered by Nekrasov and Okounkov in their study of the Seiberg-Witten Theory | ||
| + | $$ | ||
| + | \prod_{n=1}^{\infty}(1-x^n)^{\beta-1}=\sum_n\sum_{\lambda \vdash n}\sum_{v\in H(\lambda)}(1-\frac{\beta}{h_v^2})x^{|\lambda|} | ||
| + | $$ | ||
| + | $h_v$ is the hook of the box $v$ in the Young tableau of $\lambda$. | ||
| + | |||
| + | |||
==memo== | ==memo== | ||
* http://mathoverflow.net/questions/200951/nekrasov-okounkov-hook-length-formula | * http://mathoverflow.net/questions/200951/nekrasov-okounkov-hook-length-formula | ||
2015년 3월 24일 (화) 19:52 판
introduction
- expansion formula for the powers of the Euler Product in terms of partition hook lengths, discovered by Nekrasov and Okounkov in their study of the Seiberg-Witten Theory
$$ \prod_{n=1}^{\infty}(1-x^n)^{\beta-1}=\sum_n\sum_{\lambda \vdash n}\sum_{v\in H(\lambda)}(1-\frac{\beta}{h_v^2})x^{|\lambda|} $$ $h_v$ is the hook of the box $v$ in the Young tableau of $\lambda$.
memo
articles
- Han, Guo-Niu. ‘The Nekrasov-Okounkov Hook Length Formula: Refinement, Elementary Proof, Extension and Applications’. arXiv:0805.1398 [math], 9 May 2008. http://arxiv.org/abs/0805.1398.