"24차원 짝수 자기쌍대 격자"의 두 판 사이의 차이
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==관련논문== | ==관련논문== | ||
| + | * Nebe, Gabriele, and Boris Venkov. On Siegel Modular Forms of Weight 12. http://www.math.rwth-aachen.de/~Gabriele.Nebe/papers/Siemod12.pdf | ||
| + | * Borcherds, Richard E., Eberhard Freitag, and Rainer Weissauer. "A Siegel cusp form of degree 12 and weight 12." Journal fur die Reine und Angewandte Mathematik (1998): 141-153. | ||
* Erokhin, V. A. “Theta-Series of Even Unimodular Lattices.” Journal of Soviet Mathematics 25, no. 2 (April 1, 1984): 1012–20. doi:10.1007/BF01680824. | * Erokhin, V. A. “Theta-Series of Even Unimodular Lattices.” Journal of Soviet Mathematics 25, no. 2 (April 1, 1984): 1012–20. doi:10.1007/BF01680824. | ||
* Erokhin, V. A. “Theta-Series of Even Unimodular 24-Dimensional Lattices.” Journal of Soviet Mathematics 17, no. 4 (November 1, 1981): 1999–2008. doi:10.1007/BF01465457. | * Erokhin, V. A. “Theta-Series of Even Unimodular 24-Dimensional Lattices.” Journal of Soviet Mathematics 17, no. 4 (November 1, 1981): 1999–2008. doi:10.1007/BF01465457. | ||
2014년 6월 27일 (금) 19:34 판
개요
- $\Gamma\subset \mathbb{R}^{24}$가 짝수 unimodular 격자라 하자
- 루트로 생성되는 격자 $(\Gamma_2)_{\mathbb{Z}}$는 다음과 같은 24가지 경우만이 가능하다
$$ \begin{aligned} \emptyset &, & A_1^{24} &, & A_2^{12}&,& A_3^8&,& A_4^6&,& A_5^4D_4&,& D_4^6&,&A_6^4\\ A_7^2D_5^2&,&A_8^3&,&A_9^2D_6&,& D_6^4 &,& E_6^4&,&A_{11}D_7E_6&,&A_{12}^2&,&D_8^3 \\ A_{15}D_9 &,& A_{17}E_7&,&D_{10}E_7^2&,&D_{12}^2&,& A_{24}&,&D_{16}E_8&,& E_8^3&,&D_{24} \end{aligned} $$
관련된 항목들
관련논문
- Nebe, Gabriele, and Boris Venkov. On Siegel Modular Forms of Weight 12. http://www.math.rwth-aachen.de/~Gabriele.Nebe/papers/Siemod12.pdf
- Borcherds, Richard E., Eberhard Freitag, and Rainer Weissauer. "A Siegel cusp form of degree 12 and weight 12." Journal fur die Reine und Angewandte Mathematik (1998): 141-153.
- Erokhin, V. A. “Theta-Series of Even Unimodular Lattices.” Journal of Soviet Mathematics 25, no. 2 (April 1, 1984): 1012–20. doi:10.1007/BF01680824.
- Erokhin, V. A. “Theta-Series of Even Unimodular 24-Dimensional Lattices.” Journal of Soviet Mathematics 17, no. 4 (November 1, 1981): 1999–2008. doi:10.1007/BF01465457.