仿射Conway群中的对合
Involutions in the affine Conway group
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中文总结 AI 辅助
本文研究仿射Conway群的对合共轭类，证明其有9个此类类，其中一类是K3曲面Enriques对合类的类似物，用Borcherds方法计算相关双曲格正交群，发现诱导腔有无限多墙。
中文摘要 AI 辅助
仿射Conway群是Leech格的仿射等距群，该群同构于Weyl群在秩为26的偶双曲格II_{1,25}上作用的标准基本域的自同构群。本文证明该仿射Conway群恰有9个对合的共轭类，研究了它们的性质，表明其中一个类可视为K3曲面的Enriques对合类的类似物。受K3曲面和Enriques曲面潜在应用的启发，本文详细研究了由II_{1,25}中对合的不变子格导出的双曲格的正交群，该计算采用Borcherds方法完成，与此前考虑的例子不同，诱导的腔具有无限多个墙。
英文摘要
The affine Conway group is the group of affine isometries of the Leech lattice. This group is isomorphic to the automorphism group of a standard fundamental domain for the action of the Weyl group on the even hyperbolic lattice II_{1, 25} of rank 26. In this paper, we show that the affine Conway group has exactly nine conjugacy classes of involutions. We investigate their properties and show that, among these nine classes, one class can be regarded as an analogue of the class of Enriques involutions of K3 surfaces. Motivated by possible applications to K3 and Enriques surfaces, we investigate in detail the orthogonal groups of the hyperbolic lattices arising as the invariant sublattices of involutions in II_{1, 25}. This computation is carried out using the Borcherds method. Unlike the examples considered previously, the induced chambers possess infinitely many walls.
发表机构
- Graduate School of Science, Hiroshima University（广岛大学理学研究科）
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