与根系相关的θ块
Theta blocks related to root systems
摘要：
Gritsenko、Skoruppa和Zagier将根系$R$与θ块$\vartheta_R$相关联，该θ块是晶格指数的Jacobi形式。对$q$阶$1$的θ块$\vartheta_R$进行了分类，证明了它们的Gritsenko提升是奇异权的强反射Borcherds积，它与Conway群$\operatorname{Co}_0$有关.作为推论，我们得到了Gritsenko，Poor和Yuen的theta块猜想的证明，作为功能$\vartheta_R$的专门化得到的纯theta块。
英文摘要：
Gritsenko, Skoruppa and Zagier associated to a root system $R$ a theta block $\vartheta_R$, which is a Jacobi form of lattice index. We classify the theta blocks $\vartheta_R$ of $q$-order $1$ and show that their Gritsenko lift is a strongly-reflective Borcherds product of singular weight, which is related to Conway's group $\operatorname{Co}_0$. As a corollary we obtain a proof of the theta block conjecture by Gritsenko, Poor and Yuen for the pure theta blocks obtained as specializations of the functions $\vartheta_R$.
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