Traces of Singular Moduli and Moonshine for the Thompson Group
Traces of Singular Moduli and Moonshine for the Thompson Group
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汤普森群的奇异模量和 Moonshine 的踪迹
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
Brandon C. Rayhaun
中科院分区：
文献类型：
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作者：
J. Harvey;Brandon C. Rayhaun
我们描述的代表性理论的汤普森零星群和弱全纯模块形式的重量一半，出现在工作的Borcherds和Zagier的Borcherds产品和痕迹的奇异模之间的关系。我们猜想Thompson群存在一个无穷维分次模，并通过对Thompson群的每一个共轭类构造McKay-Thompson级数来证明我们的猜想，这些共轭类与高水平的权半模形式相吻合.我们还观察到一个判别属性在这个月光的汤普森组，是密切相关的判别属性假设存在于阴影月光。
We describe a relationship between the representation theory of the Thompson sporadic group and a weakly holomorphic modular form of weight one-half that appears in work of Borcherds and Zagier on Borcherds products and traces of singular moduli. We conjecture the existence of an infinite dimensional graded module for the Thompson group and provide evidence for our conjecture by constructing McKay--Thompson series for each conjugacy class of the Thompson group that coincide with weight one-half modular forms of higher level. We also observe a discriminant property in this moonshine for the Thompson group that is closely related to the discriminant property conjectured to exist in Umbral Moonshine.