"Nekrasov-Okounkov hook length formula"의 두 판 사이의 차이
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==introduction== | ==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 | * 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 | ||
| − | + | :<math> | |
\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|} | \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|} | ||
| − | + | </math> | |
| − | + | <math>h_v</math> is the hook of the box <math>v</math> in the Young tableau of <math>\lambda</math>. | |
2020년 11월 16일 (월) 10:03 기준 최신판
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
- Erik Carlsson, Fernando Rodriguez-Villegas, Vertex operators and character varieties, arXiv:1603.09267[math.AG], March 30 2016, http://arxiv.org/abs/1603.09267v1
- Jim Bryan, Martijn Kool, Benjamin Young, Trace Identities for the Topological Vertex, http://arxiv.org/abs/1603.05271v1
- Han, Guo-Niu, and Huan Xiong. “Polynomiality of Some Hook-Content Summations for Doubled Distinct and Self-Conjugate Partitions.” arXiv:1601.04369 [math], January 17, 2016. http://arxiv.org/abs/1601.04369.
- Han, Guo-Niu, and Huan Xiong. “Difference Operators for Partitions and Some Applications.” arXiv:1508.00772 [math], August 4, 2015. http://arxiv.org/abs/1508.00772.
- Pétréolle, Mathias. “A Nekrasov-Okounkov Type Formula for C.” arXiv:1505.01295 [math], May 6, 2015. http://arxiv.org/abs/1505.01295.
- Iqbal, Amer, Shaheen Nazir, Zahid Raza, and Zain Saleem. “Generalizations of Nekrasov-Okounkov Identity.” arXiv:1011.3745 [hep-Th], November 16, 2010. http://arxiv.org/abs/1011.3745.
- 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.